Probably everyone has seen or heard of the standard six-sided die. When fair (not loaded), each number from one to six has a probability of 1/6 of being the outcome in a throw.
Now imagine a die with a billion faces, or a lottery with billions of participants. The probability of each individual face or ticket becomes extremely small, but in each of these situations, throwing the billion-sided die or drawing a ticket out of the billions in the lottery is guaranteed to yield one of these extremely unlikely outcomes.
When you have a space of individual, discrete outcomes in a situation where a lack of outcome is impossible, you are certain to get one of them even if they number in the trillions. You can't, for instance, throw the hypothetical, fair billion-sided die and have it not land on one of the faces, each of which has a probability of one in a billion of showing up after a throw. You can't randomly pull a ticket from the billions in the lottery and not have a winner on your hands, unless you initially placed some blank tickets in the pool.
Why, then, should one assume that if an event is unlikely or perceived to be so, it must have been caused by an intelligent agent? For example, if wind blows over the billion-sided die and causes it to land on one of its faces, is the extremely unlikely outcome the result of intelligent planning, or is it merely the result of the certainty that a thrown die will yield an outcome when it lands no matter how unlikely said outcome is?