Probability that a triangle inscribed in an ellipse contains one of its foci

Question

Three points are chosen at random on the border of an ellipse. Those three points makes a triangle. Since ellipse has two focus points, question here is what is the probability of that triangle to contain one of those foci. I've noticed that when we take two points and draw a line through one of focus points, the third point should be in the arc where this two points lines contains to form a triangle in order to contain that focus point, then I tried to go on from angle of that two lines intersection at the focus point but since arclength varies due to change of that angle, i couldn't figure out how should I go on.