I'm reading through Jayne's Probability Theory: The Logic of Science and he mentions that given a set of propositions {$A_1A_2…A_n$} that are mutually exclusive given information $B$ (meaning, any two of them can't be true simultaneously given $B$), they can be expressed as
$$p(A_iA_j|B) = p(A_i|B)\delta_{ij}$$
What is the $\delta_{ij}$?
I would think that the probability $p(A_iA_j|B) =0$ so I'm not sure what the point of the right-hand side even is.
Best Answer
This is the "Kronecker delta". The value of $\delta_{ij}$ is $1$ when $i=j$ and $0$ otherwise.
It's not specific to probability theory.
In your example you are right to say that the right hand side is $0$ - except when $i=j$.