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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