To find the probability you need to know the number of desired outcomes (i.e. one digit only used) and the total number of outcomes.
In this case there are 3 desired outcomes - 111, 222, 333.
Since any of the 3 positions in the 3-digit number can be any of 3 numbers, there are 3 x 3 x 3 = 27 total possible outcomes.
The probability of having a desired outcome is 3 / 27 = 1 / 9 = 11.1%