Question: For a Markov chain {Xn, n 0} with transition probabilities Pi,j , consider the conditional probability that Xn = m given that the chain started

For a Markov chain {Xn, n 0} with transition probabilities Pi,j , consider the conditional probability that Xn = m 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?

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