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

(i)	$\mathcal{G} \subseteq \mathcal{F}$ is a D470: Subsigma-algebra of $\mathcal{F}$ on $\Omega$
(ii)	$E \in \mathcal{F}$ is an D1716: Event in $P$
(iii)	\begin{equation} \mathbb{P}(E) = 0 \end{equation}

Then \begin{equation} \mathbb{P}(E \mid \mathcal{G}) \overset{a.s.}{=} 0 \end{equation}

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

(i)	$\mathcal{G} \subseteq \mathcal{F}$ is a D470: Subsigma-algebra of $\mathcal{F}$ on $\Omega$
(ii)	$E \in \mathcal{F}$ is an D1716: Event in $P$
(iii)	\begin{equation} \mathbb{P}(E) = 0 \end{equation}

Then \begin{equation} \mathbb{P}( \mathbb{P}(E \mid \mathcal{G}) = 0) = 1 \end{equation}