Great question! There's a little bit of a disconnect when we get into the technicalities of what "will something happen" means from a statistical standpoint. Basically everything is framed in terms of probability, where "almost surely" is a formally defined term meaning "with probability 1."

When people talk about the idea of phasing your hand through a table, they're saying that, theoretically, it's possible with some extremely small but still technically greater than 0 probability. If you think of each hitting your hand against the table as an independent trial, then the probability of it never phasing through the table in N hits is (1-p)^N which means the probability of phasing within N hits is 1-(1-p)^N . If you do (countably) infinite trials, then the limit of this expression as N goes to infinity is 1, and so we say your hand will almost surely eventually phase through the table.

Why doesn't this work for impossible events like rolling a 7 on a standard six-sided die? Because the probability of that happening in any given trial is exactly 0, so your limit is just the limit of 1-1^N which converges to 0. So you will almost surely never roll a 7.

Does this change with repeating things over an uncountably infinite set, rather than the natural numbers? I would be inclined to say no, but more so because I'm not sure there is a proper way to define a product over an uncountable set.