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If a school has 1022 students, what chance is there if 1 student post a comment on Face Book, the comment is read by 25 people and 1 of those persons happens to be in year 12 which has 190 students and that person notices that 1 person who 'liked'the comment was running for school captain from year 11.

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    This sou$n$ds like you want to find the probability of something that really happened. As if asking "How likely is it that this weeks lottery numbers were ... and last weks were ...?" A priori the event is extremly unlikely, no matter what numbers you plug in for the dots. But you can of course plug in the *real* lottery numbers of the last two drawings and wonder how come such an unlikely event really happened?! But that's just it - it happened. Numbers from past drawings are so much easier to predict than future ones.2012-09-14

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There is no mathematical answer to this because you do not provide a probability model for (1) writing comments on Facebook, (2) for students friending each other on Facebook,(3) given a student friended someone who commented on Facebook the probability that they read and give "like" to a comment, (4) how the students distribute among the class years, and(5) how many students typically run for school captain. Also as joriki pointed out you did not make clear which event you want the probability for. I assume it is the complicated occurrence of all those things happening that you intended to specify.