Possible means it could happen. Probable means it is likely to. Everything probable is possible; most possible things are not probable. If you would put the odds above even, use probable; if you only mean the door is open, use possible.
The core difference
These mark two different points on the same scale, and swapping them changes what you have claimed.
- possible — capable of happening, however unlikely: It is possible the flight is early.
- probable — more likely than not: It is probable the flight is late.
The second sentence commits you to something the first does not. That is why the distinction matters in forecasts, medicine, law and anywhere a reader will act on the difference.
The test
Ask whether you would bet on it. If you are only saying it cannot be ruled out, the word is possible. If you would expect it to happen, the word is probable.
The scale
English gives you several rungs, and they are worth using accurately:
- conceivable — imaginable, at the very edge
- possible — could happen
- plausible — sounds reasonable, whether or not it is likely
- likely / probable — better than even
- near-certain — as close as language usually gets
Note that plausible is not a probability at all: it describes how convincing something sounds, which is why a plausible explanation can still be wrong.
The nouns
Possibility and probability follow the same split, and probability carries a mathematical sense — a number between 0 and 1 — that possibility does not. "There is a probability of 0.7" is meaningful; "a possibility of 0.7" is not.