Let \alpha and \beta be given positive real numbers, with \alpha<\beta. If two points are selected at random from a straight line segment of length \beta, what is the probability that the distance between them is at least \alpha? Please provide the value of the answer in the form simplest fraction by assuming \alpha = 1 and \beta = 2, and then giving the sum of the numerator and denominator.

Let's think step by step and output the final answer within \boxed{}.
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