What is the distribution of the distance between a specific word in a Text which is generated by a markov process?

What is the distribution of the distance between a specific word in a Text which is generated by a markov process?

For example for a text which is generated by a multinomial distribution over words, this distribution of distance will be a Geometric distribution. Thanks.

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With infinitely many states, any distribution is possible, as demonstrated by a Markov chains on $N$ which jump from $n$ only to $n+1$ or $0$.