∆ in a O - 2

A right triangle inscribed in a circle must have a diameter as its hypotenuse.

Choose point $A$ randomly. The probability of point $B$ being on the other end of $A$ 's diameter is $0$ (since choosing a specific point out of all points on the circle is a zero probability event). Similarly, if $B$ is not on $A$ 's diameter, the probability of $C$ being on either $A$ 's or $B$ 's diameter is likewise zero. $0+1\cdot0 = \boxed{0}$ .

The answer is zero because the sum of probabilities for an acute angled triangle and an obtuse angled triangle is unity. Thus there is no space for a right angled triangle.

So remember, the next time you find a right triangle in a circle, just know that it was completely accidental.