Hi, I am a quantum physicist who needs a practical help from mathematicians. The physical problem that I have can be reduced to the following mathematical problem: Assume that we have two correlated variables a and b. Assume that we know all conditional probabilities P(a|b), P(b|a) for all possible values of the variables a and b. What I want to know are all joint probabilities P(a,b). However, a priori they are not given. I want to ask the following: What is the best I can conclude about P(a,b) from knowledge of P(a|b), P(b|a)? Are there special cases (except the trivial case in which a and b are independent) in which P(a,b) can be determined uniquely? Any further suggestions? Thank you in advance!