P3391
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}
$\square$
