I have language model (LM) that produces a probability of responses A and B given a context C: P(A|C), P(B|C). Now, the prior P(A) and P(B) are different than each other: P(A) != P(B). I'm looking for a way to modify P(A|C) and P(B|C) in such a manner that considers the priors of A and B and eliminates their influence. In other words, I'm trying to compute what would P(A|C) and P(B|C) be if it held that P(A) = P(B).