The probability that Katarina will correctly solve a given Brilliant math problem is \( \frac{1}{8} \). The probability that Layla will solve the same problem correctly is \( \frac{1}{12} \). **Given that they are both incorrect**, the probability that they will give the same incorrect numerical result is \( \frac{1}{1001} \).

Suppose Katarina and Layla solve a Brilliant math problem independently and get the same numerical result. The probability that they get the correct answer, given that they got the same numerical result, can be written as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers. Find \( a + b \).

**Details and assumptions**

Clarification: When both of them solve the question correctly, they got the same numerical result.

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