Given a sample space \(\Omega\), with events \(A_1,...,A_n \subseteq \Omega\) forming a partition of \(\Omega\), with \(P(A_i) > 0\) for all \(i\leq n\), and an event \(B \subseteq \Omega\), such that \(P(B) > 0\):

\[\begin{align*} P(A_i\given B) &= \frac{P(A_i)P(B\given A_i)}{P(B)} \\ & = \frac{P(A_i)P(B\given A_i)}{P(A_1)P(B\given A_1) + \cdots + P(A_n)P(B\given A_n)} \end{align*}\]