structural:scholar_edition
Use in inference

In statistical inference, the conditional probability is an update of the probability of an event based on new information. The new information can be incorporated as follows:

This approach results in a probability measure that is consistent with the original probability measure and satisfies all the Kolmogorov axioms. This conditional probability measure also could have resulted by assuming that the relative magnitude of the probability of A with respect to X will be preserved with respect to B (cf. a Formal Derivation below).

The wording "evidence" or "information" is generally used in the Bayesian interpretation of probability. The conditioning event is interpreted as evidence for the conditioned event. That is, P (A) is the probability of A before accounting for evidence E, and P (A | E) is the probability of A after having accounted for evidence E or after having updated P (A). This is consistent with the frequentist interpretation, which is the first definition given above.