Deduction about the present

ModalCertaintyExample
must + infinitive Almost certain (positive) It must be cold — he's wearing a coat.
She must love books — she has a huge library.
should + infinitive Expectation / less certain He should be home by now — his flight landed at 5.
could / might / may + infinitive Possible (50% or less) It might rain later — look at those clouds.
She could be in a meeting.
can't + infinitive Almost certain (negative) — near impossible That can't be Tom — Tom is in Australia.
It can't be a burglar — all the doors are locked.
must vs can't: These are opposites. Use must when you are almost certain something is true: "You must be tired." Use can't when you are almost certain something is impossible: "You can't be hungry — you just ate!"
Making a deduction about the past? To guess about something that already happened (e.g. "she must have missed the train"), you need modal + have + past participle — that belongs to Modal Verbs in the Past, together with should have/could have for regret and criticism.

Certainty scale

PositiveNegativeLevel
must becan't be95% certain
should beshouldn't be~80% (expectation)
may be / might be / could bemight not be / may not be~50% (possibility)

Exercises

Choose the modal that fits the level of certainty.

1. Keiko always does really well on exams. She ___ study a lot. (almost certain)

2. That ___ be Tom at the door — he's on holiday in Australia. (almost impossible)

3. I'm not sure, but she ___ be in a meeting right now. (possible, 50%)

4. His flight landed at 5. He ___ be home by now. (expectation, ~80%)

5. Look at those dark clouds — it ___ rain later. (possible)

6. You ___ be hungry — you just had a huge lunch! (almost impossible)