[Neil Stevens]

There is no one "correct" way to interpret probabilities, and your example doesn't even work.

Assuming all the 10,793,861 people's hands are being dealt from different decks, there's actually a 37% chance that someone won't get aces all three times, by my estimate:

(10,793,860/10,793,861)^10,793,861 = about 37%

So either the interpretation is wrong, or the math is wrong, and I trust the math in this case.