Of course the odds in question are not the odds of a given hand being all spades but the odds of a hand of all spades being dealt ever. We need to know how many bridge hands have ever been dealt. I would guess that this is a highly probable event.

Case in point. The present list of birthdays has 61 people listed with definitive birthdays. Without looking, how many pairs do we have on that list? That is, how many birthdays are there that two people share?