My approach :

Number of 3-digit numbers is 999-99=900 . Number of 3-digit numbers divisible by 3 in interval [1,999] is 999/3=333.

Number of 3-digit numbers divisible by 3 in interval [1,99] is 99/3=33. Number of 3-digit numbers divisible by 3 in interval [100,999] is 333-33=300.

P=300/900=3/9=1/3.