12. For a Markov chain with transition probabilities , consider the conditional probability thatI mage given that the chain started at time 0 in state i and has not yet entered state r by time n, where r is a specified state not equal to either i or m. We are interested in whether this conditional probability is equal to the n stage transition probability of a Markov chain whose state space does not include state r and whose transition probabilities are Either prove the equality or construct a counterexample.