Consider three sets $E_1=\{1,2,3\}, F_1=\{1,3,4\}$ and $G_1=\{2,3,4,5\}$. Two elements are chosen at random, without replacement, from the set $\mathrm{E}_1$, and let $\mathrm{S}_1$ denote the set of these chosen elements. Let $E_2=E_1-S_1$ and $F_2=F_1 \cup S_1$. Now two elements are chosen at random, without replacement, from the set $F_2$ and let $S_2$ denote the set of these chosen elements. Let $\mathrm{G}_2=\mathrm{G}_1 \cup \mathrm{~S}_2$. Finally, two elements are chosen at random, without replacement, from the set $\mathrm{G}_2$ and let $\mathrm{S}_3$ denote the set of these chosen elements. Let $E_3=E_2 \cup S_3$. Given that $E_1=E_3$, let $p$ be the conditional probability of the event $S_1=\{1,2\}$. Then the value of $p$ is