Each player rolls a four-sided die which is marked 1, 2, 3 and 4 on the four sides.
Each die can turn up any of the four numbers. The probability of a four turning up when a die is rolled is 1/4 and the probability that this does not happen is 3/4. There are C(4,3) ways of choosing the dice that turn up four. The last one does not. Using this, the required probability is: C(4,3)*(1/4)^3*(3/4) = 3/64
The probability that a triple four turns up is 3/64