Mathematics · Markov Chains

Let {X n | n ≤ 0} be a homogeneous Markov chain with state space S = {0, 1, 2, 3, 4} and transition probability matrix: P = [1/4, 0, 0, 3/4, 0] [0, 1, 0, 0, 0] [1/3, 2/3, 0, 0, 0] [3/4, 0, 0, 1/4, 0] [1/8, 1/8, 1/2, 1/8, 1/8] Let α denote the probability that starting with state 4, the chain will eventually get absorbed in the closed class {0, 3}. Then the value of α is: