Modal verbs for past probability

Structure: modal + have + past participle
must have been, can't have gone, etc.

We use must have to express that we feel sure that something was true.

They must have left early.
He must have already gone.

We use can't have / couldn't have to say that we believe something was impossible.

He can't have escaped through this window. It is too small.
She can't have said that.
She couldn't have said that.

Structure: modal + have + past participle
may have been, could have gone, might have lost, etc.

We use may / could / might have to say that it was possible that something happened in the past (but we are not 100% sure).

He may have missed the bus.
The road might have been blocked.

The negatives are may not have and might not have.

He may not have left yet.
The assistant might not have received his message.