I have a small circle with area $A_s$ that is bound to be in a bigger circle with area $A_b$. The probability of the small circle being at a specific place in the bigger circle is: $$P = A_s/A_b$$
Let's say I have two of the small circles which each have a big circle. The big circles are intersecting and I'm now trying to find the probability of the two small circles colliding in the intersection area assuming that they are solid.
I know that the joint probability of both small circles being at a specific place in their own big circle is: $$P(a,b) = A_{s,a}/A_{b,a} * A_{s,b}/A_{b,b}$$
What I am now struggling with is to include the intersection area A_int into my thoughts. I did some research and got to the conclusion that I need the joint probability from above given that the intersection area is $A_{int}$: $$P(a,b|int)$$
Is my assumption correct and if so, do you have some tips on how to approach the calculation of this probability?