리 comes from the hanja 理, meaning logic, reason, or possibility. The structure V + 을/를 리가 없다 expresses disbelief in what has, is or will happen:
내일까지는 숙제를 끝낼 수 있을 리가 없어요!
There’s no way that you’ll finish your homework by tomorrow!
그는 그것을 몰랐을 리가 없어요.
It can’t be that he doesn’t know. Everybody knows.
오늘은 결혼 기념일인데 잊어 버릴 리가 없죠?!
It can’t be that my wife would forget that today is our anniversary, can it?!
그 선수는 약물을 복용하지 않았을 리가 없어요!
There’s no way that athlete didn’t take drugs!
수능일이니까 지각할 리가 없어요.
It’s the day of the Suneung so there’s no way he’d be late for school.