http://nautil.us/issue/4/the-unlikely/chasing-coincidences
"Probabilities are defined as relative measures in something called the “sample space,” which is the set of all possible outcomes of an experiment—such as drawing a card out of a well-shuffled deck, rolling a fair die, or spinning a roulette wheel. We generally assume that every elementary outcome of the experiment (any given card or any of the possible numbers, in the case of dice or roulette) has an equal likelihood, although the theory can handle sample spaces with varying likelihoods as well. If we can define a sample space in a real-world situation that may not involve a game of chance, then we can measure probabilities through this sample space.
In its essence, the idea of coincidences could be explained (somewhat simplistically) using a deck of cards. Drawing the ace of spades out of a well-shuffled deck of 52 cards is a relatively rare event: Its probability is only 1 in 52. We compute it using the mathematical rule that divides the size of the event, one card (if we’re talking about drawing
any ace, this would be a size of four), by the size of the sample space for drawing a card out of a deck, which is 52, the total number of cards.
But if every day of your life you draw a card out of a deck, you can be sure to see the ace of spades sometimes. In fact, you expect this to happen roughly once in 52 draws. It is the fact that cards can be drawn repeatedly out of a deck (with reshuffling after every draw) that makes rare events show up."