Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 $-$ S1 and F2 = F1 $\cup$ S1. Now two elements are chosen at random, without replacement, from the set F2 and let S2 denote the set of these chosen elements. Let G2 = G1 $\cup$ S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements. Let E3 = E2 $\cup$ S3. Given that E1 = E3, let p be the conditional probability of the event S1 = {1, 2}. Then the value of p is