For example , the probability of a hypothesis given some observed pieces of evidence and the probability of that evidence given the hypothesis .
Bayes ' theorem expresses the conditional probability , or `` posterior probability '' , of a hypothesis H ( i.e. its probability after evidence E is observed ) in terms of the `` prior probability '' of H , the prior probability of E , and the conditional probability of E given H. It implies that evidence has a confirming effect if it is more likely given H than given not-H .