may, might, could

To us today, people's love of the theater and their willingness to endure some hardship to indulge it may not seem terribly odd (요즘의 관점에서 본다면 자신이 좋아하는 공연을 보기 위해 이 정도의 노력을 하는 것은 그리 대단한 일이 아니다). But among the great civilizations of the day, including Persia, India, and the Middle East, as well as China, it is possible to imagine only the Greeks feeling free enough, being confident enough in their ability to control their own lives, to go on a long journey for the sole purpose of aesthetic enjoyment. The Greeks' contemporaries lived in more or less autocratic societies in which the king's will was law and to defy it was to court death. It would not have been in a ruler's interest to allow his subjects to wander about the countryside even if his subjects' ties to the land and the the routines of agriculture had allowed them to imagine going on a long journey for purposes of recreation. 
'생각의 지도'에서

어떤 일이 일어나고 있거나 앞으로 일어날 가능성에 대해 언급할 때 may, might, could를 쓴다. 부정문에서 쓸 때는 may/might not과 couldn't의 의미가 다른점에 주의해야 한다. 

She may not be at home. 
그녀는 집에 없을지도 모른다. (Perhaps she is not at home)

I could not complete the project last week because I was busy.
지난주에 바빠서 프로젝트를 끝내지 못했다. (impossibility)

또 어떤 일이 확실하다고 단정할 때 must, 그리고 확실성을 부정하여 '~일 리가 없다'라는 의미로는 can't을 쓴다. 

It can't be Craig at the door. He is in the States. 
Craig이 왔을 리 없어. 그는 미국에 있잖아. (certainly not)