Let S be the sample space of all 3 × 3 matrices with entries from the set {0, 1}. Let the events E_{1 }and E_{2} be given by

E_{1 }= {A ∈ S : det A = 0} and

E_{2} = {A ∈ 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 ___