Let S be the sample space of all $3 \times 3$ matrices with entries from the set $\{0,1\}$. Let the events $\mathrm{E}_1$ and $\mathrm{E}_2$ 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 $\mathrm{P}\left(\mathrm{E}_1 \mid \mathrm{E}_2\right)$ equals $\_\_\_\_$