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
$$E_1 = \left\{A \in S : \det A = 0\right\}$$ and
$$E_2 =$$ {$$A \in S$$ : sum of entries of A is 7}.
If a matrix is chosen at random from S, then the conditional probability $$P(E_1|E_2)$$ equals _______