Possibility indicates that something might happen, that there is a chance that something will happen.

Probability indicates that something is very likely to happen.

In talking about the present and the future, people use different modal auxiliary verbs to indicate how probable they think a certain event is.

Azar*, for example, describes certain modal auxiliaries in this way:

may – less than 50 % certainty Where's John? He may be at the library. [The speaker is not sure. Maybe John is at the library, or maybe he is somewhere else.]

might – less than 50 % certainty Where's John? He mightbe at the library. [The speaker is not sure. Maybe John is at the library, or maybe he is somewhere else.]

could - less than 50 % certainty Where's John? He could be at the library. [The speaker is not sure. Maybe John is at the library, or maybe he is somewhere else.]

should – 90 % certainty She should do well on the test. [She is an excellent student, and what's more, she has studied hard for this test.].

must – 95 % certainty [about the present]. Mary isn't here. She must be sick. [Yesterday Mary was coughing and sneezing and went home early because she didn't feel well.]

(In the examples above, the sentences in the brackets were added by me for clarity in this short explanation.)

Rachel
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*Understanding and Using English Grammar, Third Edition, by Betty Azar. Longman. 2002

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