I was bored, so I did the math. Apparently, there's a 0.75 probability of there being a civvy cop. Same probability for there being a civvy doc. (according to hypergeometric calculator with: pop = 20 roles, nr successes = 1, sample size = 15 - for 15 civvy - , nr successes in sample = 1)
So that leaves us with 0.75 * 0.75 = 0.5625 probability of having both civvy cop and civvy doc. Then the probability of both existing AND the doc hitting the cop is 0.5625 * (1/17) = 0.03308823529 ~= 0.033.
So that leaves us with 3.3% chance.
Of course, all this information is worthless, but as said, I was bored.