We can use some modal verbs with the past participle of the main verb:
modal + (not)+ have + past participle
You could have hurt yourself.
They should have warned me.
He must have got lost.
It is the same form as in the third conditionals.
We use modals this way when we are talking about the past situation that can't be changed.
Meaning of past modals
|could have done
||something was possible in the past or there was a probability, but it didn't happen
||He could have slept till evening but the alarm clock woke him up.
|should have done
||it was a good idea to do that, but it didn't happen
||You should have told me that the meeting was cancelled.
|must have done
||it is very likely that somebody did something
||Where are my gloves? I must have left them in the car.
|might have done
||it was probable
||They might have misunderstood us.
|would have done
||something was possible, but it didn't happen
||I would have telephoned that company, but there wasn't a phone number on their website.
Try to express probability using modal verbs instead of long complex sentences like "It is possible that..." / "It is probable that..." / "I am sure that...". The shorter is the sentence, the "more English" it sounds.