Context: There are two lecturers in the particular faculty in the university and both of them are teaching the same subject as two parts. The first lecturer completed his part and the second lecturer is taking classes nowadays.
During a class, the second lecturer is telling [he is in doubt - 50/50] that the first lecturer [should have/might have/would have] taught this section in his classes.
So what would be the ideal modal verb for this situation and why others are not appropriate?