"just because something can be shown to have a mathematical probability of happening doesn't mean it has a corresponding possibility in reality."
Yes but I wonder if that is specific enough. Like in the monkey analogy people seem to default to a position that "anything is possible but the possibility may be infinitesimally small." Well, but that's the question, isn't it? is there really ANY possibility of certain things happening, and can't we be pretty confident in saying that some things can never happen, and shouldn't we try to be rigorous in separating the two? If we think about the monkeys that exist in reality, even given an infinite time I would not expect them by nature to be interested in hitting all the keys randomly and persistently enough to come up with a sonnet.
The "anything is possible" cliche is a dangerous one, I'm thinking.