CareerCup

Case 1) all 3 white caps: Impossible as per one of the clauses
Case 2) 1 blue 2 white: Unfair, because the one with the blue cap wins. So impossible.
Case 3) 2 blue 1 white: Two of them see 1 white and 1 blue. They are sure that they cannot have a white cap. Because then the one having blue cap will win. Then the one with the blue cap will always lose and one of the other two wins. So Unfair and impossible.
Case 4) 3 blue caps. Only possible option.

We know that

WWW would be wrong because this violates 2
We know that

BWW would be unfair because the person who sees both whites would win.

The only way this would be generalized to all 3 is if all 3 wore blue hats.

So,
BBB

Explaining case 3) 2 B 1 W: Two of them see 1 white and 1 blue. They are sure that they cannot have a white cap. Because then the one having blue cap will win. So 2B 1W is fair for the two employees. But this is unfair for the other single employee. Because in 2B 1W he always loses. So 2B 1W is unfair and impossible.

@s100banerjee
The posted answer is correct. But there is a mistake in the explanation for Case 3

Case 3) 2 blue 1 white: Two of them see 1 white and 1 blue. They are sure that they cannot have a white cap. Because then the one having blue cap will win. Then the one with the white cap (not blue cap) will always lose and one of the other two wins. So Unfair and impossible.