If $A$ and $B$ are vertices of a polyhedron, define the distance $d(A,B)$ to be the minimum number of edges of the polyhedron one must traverse in order to connect $A$ and $B$. Let $Q,R,$ and $S$ be randomly chosen distinct vertices of a regular icosahedron. What is the probability that $d(Q,R)=d(R,S)$?