A drawer contains \( 200 \) distinct pairs of socks, and three socks are chosen at random. The probability that the three socks contain a pair of socks is \( \frac{a}{b} \), where \( a \) and \( b \) are coprime positive integers. What is the value of \( a+b\)?

**Details and assumptions**

The pairs are distinct, which means that no two pairs are the same.

Within a pair of socks, the left sock matches the right sock, and thus forms a pair.

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