The problem ultimately reduces to this: given a chosen ball X, find the probability of each urn with n balls being the one that represents the universe. If you had a limited number of urns, you'd add up the probabilities and multiply by a normalization factor to account for the fact that at least one urn must be chosen. Even with an infinite number of urns, if you have a finite sum, you can still normalize with a finite factor. However, because the series is divergent as the upper bound of n tends to infinity, the probability of each urn being chosen is essentially zero.

Carter claims that a 10 ball urn is more likely than a million ball urn. That may be true, but it is not more likely than an urn with between a million and fifty million balls. And so it goes. You can always find a range of urns that is more likely than the last. And that's where his error lies.