Fred is likely to win the election. Fred is apt to win the election. Fred is liable to win the election.
But these three words do have some subtle distinctions in meaning.
Under traditional rules, use liable only if the subject of the sentence will be adversely affected by the event expressed by the infinitive phrase. Thus:
Fred is liable to lose the election.
The word likely is much more general than either liable or apt. Use likely when you don’t want to pin any fault on, or assign any property to, the subject of the sentence. Thus, if you say that Fred is apt to lose the election, you intimate that Fred is somehow responsible. But if you say that Fred is likely to lose the election, then you’re merely predicting the outcome and not suggesting the reasons for the loss. Further, the use of likely doesn’t ascribe any negative reaction Fred might have about the loss.
Example: He is likely to try that again, and judging from his history, I’d say he’s apt to succeed, unless he looses focus, in which case he is liable to fail.