Conditional Probability of Matching Colors

A jar contains 3 red balls, 4 blue balls, and 3 green balls. Isaiah takes three balls from the jar at random without replacement. Given that one of the balls taken this way is red, what is the probability that the two other balls have the same color? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.