A cricket randomly hops between $4$ leaves, on each turn hopping to one of the other $3$ leaves with equal probability. After $4$ hops, what is the probability that the cricket has returned to the leaf where it started? Express your answer in the form \(\frac{k}{m}\) where the fraction is in simplest form, and find the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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