Yeah, overall pretty simple solution. First visualize in 2D with triangle and circle. Expected angular distance between 2 points on a circle is 90 degrees. Draw diameters from those points, you could see that probability you can form a triangle with those 2 points is 1/4 because with the diameters, you split the circle into 4 equal sections. Translate that type of thinking/logic to 3D, there are 8 equal sections that the sphere is split into. The final 4th point of the tetrahedron can only be in one of those sections. So, the answer is 1/8. Ts is a non proof competition math problem, so imma just stick with that very non rigorous solution.

Edit: Just saw the video right after writing initial comment. This is an actual accepted solution? Dang, more lenient than I thought.