Total of 3-digit numbers=1000-111=889 (111, 112, ..., 998, 999).
Total of all 3 digits the same=9 (111, 222, ..., 999).
Total of 2 digits only the same=9*8=72 (112, ..., 119, 221, 223, ..., 229, ..., 998) multiplied by 3 for all different permutations (e.g., 112, 121, 211; 225, 252, 522)=216.
Probabilities are these figures divided by 889.
Probability of all digits the same=9/889=0.0101 or 1.01% approx.
Probability of 2 digits the same=216/889=0.2430 or 24.3% approx.
Probability of no digits the same=(889-216-9)/889=664/889=0.7469=74.69% approx.