Let \(S = \{ S_1, S_2, ... , S_m \}\) where the \(S_k\) are pairwise disjoint and \(S_1 \cup S_2 \cup ... \cup S_m = S\) (i.e. a partition of the space S). Then for any \(A \subseteq S\)
\begin{equation*}
P(S_j | A) = \frac{P(S_j)P(A | S_j)}{\sum_{k=1}^m P(S_k)P(A | S_k)}.
\end{equation*}
The conditional probability \(P(S_j | A)\) is called the posterior probability of \(S_k\text{.}\)