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.
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.