JEE Math Practice Question

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 what is the conditional probability $P\left(E_{1} \mid E_{2}\right)$?