Sample space is 20^3 triples (xl,x2,x3), in which each xi is in [1,2, .... ,20].
Each triple has weight 1/ (20^3) .
The required probability is P(A)=l·P(B), where B is the event in which all three keys hash to different locations i.e. no collision.
P(B)= 20 * 19 * 18 / 20^3 = 0.855, Hence P(A)= 1- 0.855 = 0.145