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It does apply. Someone has to be the oldest. Someone has to be the oldest-person who has the largest gap. Regardless of how old that is, or how large the gap is, there will be at least one.

Ok, now I get the point you were trying to make.

The lottery parallel still doesn't feel the most apt; the definition you specify ensures that you will always have such a person (who lived to be the oldest, and who had the largest gap with the previous record holder) for n > 1 people. In that sense it is recurrent, unlike winning the lottery, which no one has until someone does (or winning in a raffle, where we know that there will aways be a winner due to the very definition of the game).

Regardless, none of that helps us determine any further how plausible Calment's statistically anomalous record is.

Someone has to be the oldest but the gap is an independent information. Mortality rate is constant at 0.5 per year for Supercentenarians. That gap is a massive outlier.

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