Markov Chains & Long-Run Behavior · Challenge problem

A random walk moves on the vertices $A, B, C, D$ of a weighted graph whose edges are $AB$ with weight $1$, $BC$ with weight $2$, $CA$ with weight $3$ and $CD$ with weight $4$. From its current vertex the walker moves along one of the edges at that vertex, chosen with probability proportional to the edge's weight. In the long run, what fraction of all steps are moves from $C$ to $D$? Express your answer as a common fraction.