Look up!

Four people play a game wherein they stand in a circle (or in this case four corners of a square) all look down, and then they all look up at the same time and into one of the other three people's eyes randomly.

If the probability that at least two people will look at each other is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?


Image credit: http://bradhallart.blogspot.com/
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