Chain rule and conditional probability

Question

I know $$ P(B|A,C) = \frac{P(A,C|B)\cdot P(B)}{P(A,C)} $$ by Bayes Rule. But how can $P(A, C|B)$ be simplified further?

Will the chain rule for conditional probability also work?

Answer 1

To me, the simplest formula for $P(B|A,C)$ is $P(A,B,C)/P(A,C)$. The other expressions are just variations on this one.