Probability of Choosing Consecutive Terms

From the first $12$ positive integers, Elphaba chooses three of them at random without replacement. What is the probability that the three positive integers chosen this way, when arranged in increasing order, are consecutive terms of an arithmetic progression? The answer is in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are coprime positive integers. Input the value of $\alpha + \beta$.