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

(i)	$E \in \mathcal{F}$ is an D1716: Event in $P$
(ii)	\begin{equation} \mathbb{P}(E^{\complement}) > 0 \end{equation}

Proceeding from the definition, we have \begin{equation} \mathbb{P}(E \mid E^{\complement}) = \frac{\mathbb{P}(E \cap E^{\complement})}{\mathbb{P}(E^{\complement})} = \frac{\mathbb{P}(\emptyset)}{\mathbb{P}(E^{\complement})} = 0 \end{equation} $\square$