-(으)ㄹ 리가 없다

In Korean, the construction -(으)ㄹ 리가 없다 means "it cannot be that [...]." It can be used to express surprise.

Etymology

The word 리(理)理 is spelt as 이 when found at the beginning of a compound, but as 리 on its own or non-initially. means "logic," "way," or "reason."