30 minutes ago, dimreepr said:

I was thinking in terms of the universe and the space it takes up, I think, as in an infinite boundary does not = infite monkey's.

My apologies for not understanding the math to explain myself more correctly or fully understand your point, but thanks for your patience.

I think you're getting confused here. Space itself is not of a statistical nature. Things going on in space are. Space is just a backcloth of everything else.

You cannot set up a proper statistical question that involves only space with nothing in it. Wally can be here or Wally can be there. But there's nothing to be done with here and there without some kind of Wally.

16 hours ago, studiot said:

ou need to be careful in your specification of 'an event'

That is correct.
So if the question specifies the event
"what is the probability of any one horse winning the race" then

18 hours ago, MigL said:

In effect, the probability of any one of the horses winning the race is 1/6 .

Of course you can ask "what is the probability of any event happening", which would also include a dead heat, all disqualified, and many more; but that is not what was asked.
Just as in @joigus' original post, the paradox is in the wording of the question; not with the probabilities themselves.