When to Apply Bayes' Theorem

The sample space is partitioned into a set of mutually exclusive events { A1, A2, . . . , An }.
Within the sample space, there exists an event B, for which P(B) > 0.
The analytical goal is to compute a conditional probability of the form: P( Ak | B ).
You know at least one of the two sets of probabilities described below.

P( Ak ∩ B ) for each Ak
P( Ak ) and P( B | Ak ) for each Ak