  The most important fact about conditional probabilities is undoubtedly Bayes' Theorem, whose significance was first appreciated by the British cleric Thomas Bayes in his posthumously published masterwork, "An Essay Toward Solving a Problem in the Doctrine of Chances" (Bayes 1764).  Bayes' Theorem relates the "direct" probability of a hypothesis conditional on a given body of data, PE(H), to the "inverse" probability of the data conditional on the hypothesis, PH(E).