In probability theory, the prior and conditional probabilities
of two random events are related by Bayes' theorem. The theorem is
often used when we have observations and wish to compute posterior
probabilities.

For example, given an observation that a patient is seen to have certain
symptoms, we can use Bayes' theorem to compute the probability that a
suggested diagnosis is correct.

P(A) is the prior probability of A. P(A|B) is the conditional probabilty
of A given B. P(B|A) is the conditional probabilty of B given A. P(B) is
the prior probability of B, and must be non-zero. Bayes' theorem is given
by P(A|B) = (P(B|A)P(A))/(P(B)).