probability question

Look at the diagram:

Find angle $\alpha$ using the cosine rule    (i.e. $cos(a) = (b^2 + c^2 - a^2)/(2bc)$ )

Take the ratio of the arc of the circle subtended by $2\alpha$  to that of the circumference of the whole circle to get the probability.

i.e. probability = $2\alpha / (2\pi)$

(Note that the lower point could be on the opposite side of the circle hence $2\alpha$ not just $\alpha$)