Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
| (i) | $X, Y : \Omega \to \Xi$ are each a D202: Random variable on $P$ |
| (ii) | $X, Y$ is an D2713: Independent random collection on $P$ |
| (iii) | $\{ X \in E \} \in \mathcal{F}$ is an D1716: Event in $P$ |
Then
\begin{equation}
\mathbb{P}(X \in E \mid Y) = \mathbb{P}(X \in E)
\end{equation}