> at some point there is really no difference between impossible and 'incredibly small probability'.
This is not true.
Using your air molecules example: Every microstate (i.e. location and speed of all the molecules) possible under the given macrostate (temperature, number of molecules, etc) has a probability of happening of 0, but aren't impossible, simply because the microstates are real variables and real numbers are uncountable. Impossible microstates also have 0 probability but are obviously not the same.
A bit late, but if you do consider events with vanishingly small probability to be impossible then they do become equal.
It's just that you then have to contend with the paradox that impossible events happen all the time, just not the ones you had in mind.
I mean sure it is possible for all air molecules to randomly all go to the same corner of the room at the same time (heck it is inevitable in some sense), you can play it back in reverse to check no laws of physics were broken, but practically that simply does not happen.