Your first version is not clear. There are still a few problems with the second. First, assessing the probability that the members of the small organization know each other, and second whether knowing one another in the small group and attending the large are independent events, and third if the number of people met by those at the large group not in the small group also has a mean of 50.

If I may assume that each of the 1,000,000 also meets 50 people, you have 50,000,000 possible dyads, and the 9000 becomes irrelevant as you've explained it. If 500 "special" people attend who meet 50 people each, that's 25,000 possible dyads. You could choose a different 500 from the 9000, but if they are each equally likely to know one another it will not change the probability. There's still the first two problems, but the simple answer is (dyads with both members from small organization)/(total dyads), 25,000/50,000,000 = 0.0005 as a max, reduced by probability of each member knowing one another.

If knowing one another is independent of being in both organizations (doubtful), you just multiply, otherwise you need to know either the probability of knowing one another and the conditional probability of being in both organizations given they know one another, or the probability of being in both organizations and the conditional probability of knowing one another given they're in both organizations.