A bag contains \(150\) balls numbered \(1\) through \(150\). Three balls are drawn and placed on the table. The probability that the balls were drawn in increasing order can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

**Details and assumptions**

The balls are drawn **in increasing order** if each subsequent ball is a higher number. As an explicit example, drawing balls \( 1, 10, 100 \) in that order is considered an increasing order.

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