Consider all the different one-ace hands you could have been dealt, and all the more-than-one-ace hands you could have been dealt. The odds of two or more aces, given at least one ace, is the size of the second set divided by the size of the first set.

Now restrict the hands to those that contain the ace of spades. This eliminates all but one fourth of the one-ace hands. But more than half of the two-or-more-ace hands have an ace of spades in them, so we keep most of the second set. So whatever the odds were in the case where any ace would do, they are better now (in fact they've more than doubled).

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