though it is probabilistic in nature, my understanding is it not like a probability of one event in infinite time. Rather a sequence of events within a interval; with a specific initial condition.   Also many players are trying at the same time and the first one wins.  In other words it is not getting one time head in coin toss but getting a specific sequence say hhhhhtttthth within a minute before some one else gets it. That is my understanding. Also I think there is a further complication that you need a previous bitcoin and a transaction to mine the next one. If that is true no one can mine all coins in isolation.