You could think of it this way: We're counting the interval after each quake before the next one happens.

If one happens after a certain interval, say 3 days, it is no longer possible to have a longer interval.

So the third of the events that have another event within a day cannot have an interval longer than a day, the third of the other two thirds that have an event in the following day cannot have an interval longer than two days, etc.

Which leads to a distribution 1/3, 2/9, 4/27, 8/81, ... with each day stepping down by a third in a geometric series.