Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$H, E_1, \ldots, E_N \in \mathcal{F}$ are each an D1716: Event in $P$
(ii)	$E_1, \ldots, E_N$ is a D5143: Set partition] of $\Omega$
(iii)	$\mathcal{G} = \sigma \langle E_1, \ldots, E_N \rangle$ is a D318: Generated sigma-algebra on $\Omega$ with generators $E_1, \ldots, E_N$

Let $n \in 1, \ldots, N$ be a D996: Natural number such that

(i)	\begin{equation} \mathbb{P}(E_n) > 0 \end{equation}

Then \begin{equation} \forall \, \omega \in \Omega \left( \omega \in E_n \quad \implies \quad \mathbb{P}(H \mid \mathcal{G})(\omega) = \frac{\mathbb{P}(H \cap E_n)}{\mathbb{P}(E_n)} \right) \end{equation}

Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$H, E_1, \ldots, E_N \in \mathcal{F}$ are each an D1716: Event in $P$
(ii)	$E_1, \ldots, E_N$ is a D5143: Set partition] of $\Omega$

Let $n \in 1, \ldots, N$ be a D996: Natural number such that

(i)	\begin{equation} \mathbb{P}(E_n) > 0 \end{equation}

Then \begin{equation} \forall \, \omega \in \Omega \left( \omega \in E_n \quad \implies \quad \mathbb{P}(H \mid E_1, \ldots, E_N)(\omega) = \mathbb{P}(H \mid E_n) \right) \end{equation}