Geometric probability

Let the side of the triangle be $2s$

The area of "success" is a $60 ^ \circ$ sector of a circle centered at Point A, and the radius is half the side length of the triangle. 

The total area is the area of an equilateral triangle. 

Can you take it from here?

Thanks Builderboi.

Here is another way of looking at it.

Since it is a equilateral triangle, the point is just as likely to be closer to A as it is to be closer to B

what does that tell you.