Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) | $\text{Observation}, \text{Assumption} \in \mathcal{F}$ are each an D1716: Event in $P$ |
(ii) | \begin{equation} \mathbb{P} (\text{Observation}), \mathbb{P} (\text{Assumption}) > 0 \end{equation} |
Then
\begin{equation}
\mathbb{P}(\text{Assumption} \mid \text{Observation}) \mathbb{P}(\text{Observation}) = \mathbb{P}(\text{Observation} \mid \text{Assumption}) \mathbb{P}(\text{Assumption})
\end{equation}