Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{ 0,1 \}$. Let the events $E _ { 1 }$ and $E _ { 2 }$ be given by
$$\begin{aligned}
& E _ { 1 } = \{ A \in S : \operatorname { det } A = 0 \} \text { and } \\
& E _ { 2 } = \{ A \in S : \text { sum of entries of } A \text { is } 7 \} .
\end{aligned}$$
If a matrix is chosen at random from $S$, then the conditional probability $P \left( E _ { 1 } \mid E _ { 2 } \right)$ equals $\_\_\_\_$