How odds are set is a really interesting subject that I have done some research into, and in a similar way sports analytics.
The first paper I would refer to covers the NFL specifically "Why are Gambling Markets organised so differently from Financial Markets", Steven.D.Levitt (The Economic Journal 2004). This illustrates that the odds on the NFL are rarely set to generate 50/50 action because the bookmaker can exploit "square" action by skewing odds against their traditional bias (i.e. the point made above about the Ohio State Buckeyes - if the bookmaker is aware that they are going to take a larger % of the bets, they can either adjust the odds or the spread so the better has to pay a premium to bet the Buckeyes - e.g. the -7.5 or more than one touchdown instead of -6.5 - especially if the true rating for the game was around -5 or -6). It also makes the point that bookmakers/sportsbooks rarely make the odds themselves they are usually paying influential odds makers who set the line for a lot of events. The bookmaker will then rarely adjust these odds greatly as they will effectively handicap the market against other bookmakers and sportsbooks (generating a profitable opportunity for "sharp" action).
In the case of the game quoted by the OP, the prices quoted by Bet 365 is consistent with the over-round % that they have run on most football games this season of between 105-107% (I have an interest in this - their over-round% on the English Premier League is typically 5-6%). That 5-7% margin will look after them in the long run as it increasingly means unsophisticated gamblers have to be more right than average in the long run to make a a sustained profit. How the actual odds are generated is another matter in the case of Bet365 a lot of their competitors use the Bet Genius group for Odds Data (e.g. Sportingbet, Paddy Power, Sky Bet). They will probably then make small adjustments to this based on their typical clients betting preferences (e.g. what type of action they take and biases).
For a lot of sports the Cantor Fitzgerald group have created the Midas Algorithm to set up odds in the same way they would deal on Wall Street and they are getting an increasing presence in Las Vegas running several sports books - http://m.wired.com/magazine/2010/11/ff_midas/all/1. This has allowed them to set spreads for the entire NFL season (http://www.grantland.com/blog/the-triangle/post/_/id/27740/nfl-win-totals-hot-off-the-sportsbook-press) before the pre-season has taken place (which is not a typical case as most bookmakers seems to react on week to week action and player injuries and performance).
How are the actual odds generated? This is the more difficult question. Going on Mathletics (Wayne L.Winston 2009), some sports e.g. the NFL can be governed by a simple least squares algorithm based on margins of victory and points scored which can then be finessed (e.g. to give more weight to recent games). This can then be used to generate win percentages based on the ratings derived. In the case of the NFL, Hal Stern "On the Probability of Winning an American Football Game" (American Statistician 45, 1991) showed that the probability of the final margin of victory for home NFL team can be well approximated by a normal random variable with mean = home edge+home team rating-away team rating and a standard deviation of 13.86. Plug the ratings generated by your least squares work in and you have a set of percentages against a given spread. I believe that this can also be applied to a lot of other sports (e.g Australian Rules Football). In the case of football though I believe that oddsmakers also have done some regression analysis into player statistics to allow them to make a more rational rating based on the players that will actually be on the pitch rather than past team performance in terms of margins of victory (e.g. the Dtech group who analyse European football for the Times Newspaper base their ratings on the Team shots and goals data http://www.dectech.org/football/help_info.php - rather than a least squares model based purely on margin of victory). Given that sports could and should be viewed as an academic subject, I believe this is why we have seen increases in the number of the groups such as the Accuscore group who have a largely academic background (from interviews on the ESPN Behind the Bets Podcast) and have used their knowledge to generate opportunities from odds skewed to exploit gamblers that bet with pre-conditioned biases (e.g. the home team favourite wins more than 50% of games). If you can remove bias from the team that you pick, I believe this will generate opportunity.
Imagine that you threw your fair six-sided die and you got ⚀. The
result was so fascinating that you called your friend Dave and told
him about it. Since he was curious what he'd get when
throwing his fair six-sided die, he threw it and got ⚁.
A standard die has six sides. If you are not cheating then it lands on each side with equal probability, i.e. $1$ in $6$ times. The probability that you throw ⚀, the same as with the other sides, is $\tfrac{1}{6}$. The probability that you throw ⚀, and your friend throws ⚁, is $\tfrac{1}{6} \times \tfrac{1}{6} = \tfrac{1}{36}$ since the two events are independent and we multiply independent probabilities. Saying it differently, there are $36$ arrangements of such pairs that can be easily listed (as you already did). The probability of the opposite event (you throw ⚁ and your friend throws ⚀) is also $\tfrac{1}{36}$. The probabilities that you throw ⚀, and your friend throws ⚁, or that you throw ⚁, and your friend throws ⚀, are exclusive, so we add them $\tfrac{1}{36} + \tfrac{1}{36} = \tfrac{2}{36}$. Among all the possible arrangements, there are two meeting this condition.
How do we know all of this? Well, on the grounds of probability, combinatorics and logic, but those three need some factual knowledge to rely on. We know on the basis of the experience of thousands of gamblers and some physics, that there is no reason to believe that a fair six-sided die has other than an equiprobable chance of landing on each side. Similarly, we have no reason to suspect that two independent throws are somehow related and influence each other.
You can imagine a box with tickets labeled using all the $2$-combinations (with repetition) of numbers from $1$ to $6$. That would limit the number of possible outcomes to $21$ and change the probabilities. However if you think of such a definition in term of dice, then you would have to imagine two dice that are somehow glued together. This is something very different than two dice that can function independently and can be thrown alone landing on each side with equal probability without affecting each other.
All that said, one needs to comment that such models are possible, but not for things like dice. For example, in particle physics based on empirical observations it appeared that Bose-Einstein statistic of non-distinguishable particles (see also the stars-and-bars problem) is more appropriate than the distinguishable-particles model. You can find some remarks about those models in Probability or Probability via Expectation by Peter Whittle, or in volume one of An introduction to probability theory and its applications by William Feller.
Best Answer
The collection of odds (which I will call 'the book') are set up so bookies will make a profit.
As the bets come in, those odds have to shift in response, to keep the book in profit, so a given bet placed at one time will get different odds than a bet placed at a different time.
A second factor: if bookies offer odds too different from other bookies, they may experience punters exploiting that by 'making a book' of their own. So they tend to pay very close attention to other bookmakers odds and adjust in response.
If a bookie gets a bet large enough to eat their profits if it wins, they may attempt to 'lay off' a chunk of the bet with other bookmakers.
In some sporting events, the use of point-spreads comes into the calculations, either in place of or along with over-round, depending on the situation.
These days the whole book can be managed by computers. (If they're working with point-spreads, there may be some more-or-less formal model for the point-distribution of the two sides that will update over time. It may include whatever factors it occurs to them to include. Such information tends to be secret, since telling people too much information about your models will make you more easy to exploit, and there's a lot of money involved.)
You may find the following details of some help Making a book and Spread betting.