Three logicians

Puzzle

Three logicians are chatting after teaching their classes for the day. As they talk, each notices that the other two have smeared dry-erase marker on their face, and all three begin laughing at each other. Of course, none of the logicians can see their own face. After a minute, the most senior and well trained logician stops laughing, having realized that her own face is smeared. How did she know?

See also

Green eyed dragons - Same idea, but with 100 dragons.