See, it's like this: if I throw a coin into a circle, what's the chance it's gonna land on any side? Well, damn near one. (It might land on the edge...)
If I toss a handful of coins onto the table, with a four-inch circle drawn on it, what's the chance a coin will land in it? Pretty good, probably. Less than the example above, though.
If I toss a handful, what's the chance the coin that lands in the circle is a penny? S'pose it depends on what change I have, but surely much, much smaller than the above.
And that the penny lands face up? Smaller still.
But if I toss the coins, and a penny lands face-up in the circle, is that miraculous? Not overly.
Picture your life as being the result of trillions upon trillions of coin-tosses with millions of available circles. Even though the chance of your series of coins landing where they did may seem infinitessimally small, the chances that coins would land in the circles is still pretty good, comparably speaking.
If I take a deck of cards and toss it towards a seven-card outline, chances are that nothing interesting is going to land. But it is entirely possible that a royal flush will land right in the outlines. The chance may be infinitessimally small, but it might. Now, if those outlines were somehow designed to catch the cards... then something would land in those seven cards. It might be gibberish, or it might be a royal flush, or it might be a straight or a full house... but the chances of any one of them landing is exactly equal to the chance of any other one landing (barring the distribution of cards, of course). The fact that it happens to land as a royal flush is no more nor less significant than the chance it might have landed as crap.
With life, we're dealing with a series of low-probability events manifesting over time. But we're also dealing with an unimaginably vast universe and a nearly incomprehensible amount of time. Chances are, it was bound to have happened. Chances are, it's happened again somewhere.
In a vast universe, any non-zero chance could manifest. In an infinite one, it would have to manifest somewhere.
Here's a real mind-blower, Ian: over the course of time, if we assume infinite time and space, there's bound to be an infinite number of incarnations of 'you' (or, more correctly, someone just like you). Luckily for us, species tend to die off eventually.