Walk one round

A 4 digit number is randomly picked out of all the 4 digit number. Find the probability that the product of its digits is divisible by 3. If the answer can be expressed as \(\large\frac{a}{b}\) for coprime positive integers \(a,b\), what is the value of \(a+b\)? This problem is part of the set Advanced is basic

Note: 012 is a two digit number, not a three digit number.

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