In doing an expert task, such as medical diagnosis, the goal is to determine identifications (diseases) given observations (symptoms). Bayes' Theorem provides such a relationship.
P(A | B) = P(B | A) * P(A) / P(B)
Suppose: A = Patient has measles, B = has a rash
Then:
P(measles/rash) =
P(rash/measles) * P(measles) / P(rash)
The desired diagnostic relationship on the left can be calculated based on the known statistical quantities on the right.