Here is the probability of having a 4-digit PIN without any number repeating.
Permutation of 4-numbers without repetition is:
10P4 = 10!/(10-4)! = 10 x 9 x 8 x 7 = 5040
Total number of combinations possible from 4 digits:
nr = 104 = 10000.
Probability = 5040 / 10000 = 0.5
