Four is a crowd

Discrete Mathematics Level pending

Three points are chosen uniformly at random within a unit circle in the \(xy\)-plane.

A fourth point is chosen uniformly at random on the perimeter of a circle with radius \(r\).

For \(r >> 1\), (say \(r \approx 1,000,000,000\)), what does the probability \(p\) that the four points form a convex quadrilateral approach?

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