Suppose we run the rich$-$get$-$richer process $($p$.547)$ to produce a graph on four nodes, with the nodes arriving in the order $1,2,3,4,5.$ For nodes $2,3,4,$ and $5$ the probability of choosing a node to link to uniformly at random is p $=1/4$ and the probability of choosing an earlier node and copying their decision is $1-$p $=3/4.$ Each of nodes $2,3,4,$ and $5$ creates one outgoing link. We will assume in this process that if a node chooses to copy the decision of node $1,$ then this just means linking to node $1.$ What is the probability that, after the process completes, node $1$ has all four incoming links, i$.$e$,$ that nodes $2,3,4,$ and $5$ all link to node $1?$