In a random sequence of double-stranded DNA, the probability that there are exactly n nucleotide pairs between two successive occurrences of a short sequence motif is given by (1 - x)nx, where x is the probability of occurrence of the motif along the sequence. When x = 1/512, the mean distance between occurrences is 512 nucleotide pairs. What is the probability that the distance between two occurrences is exactly equal to this mean?
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