Say A is a standard normal and B is a random variable that can take values 1 and -1 with the same probability. If I say C = A+B and I fix B for the value 1, I can say C = A+1, which gives me the conditional PDF of C given B=1. I can do the same if I fix B for the value -1. I'm looking for an expression of the inequality P(B=1|C=c) > 2*P(B=-1|C=C)