If the infinite multiverse theory is correct, then not only is life probable, it's certain. When you're working with infinity any finite chance of occuring will occur an infinite amount of times.
People assume there must be a designer because they don't understand probability. Lets say i generate a random number between one and ten million (i will in fact do this now), and that number turns out to be 645,231. There was a one in ten million chance of 645,231 being the number that cropped up, yet there it is.
Each individual number has a tiny chance of occuring, but the chance of a number occuring is certain. The same could well be true for life; the probability of the specific life known as humans is minute, the probability of a form of life is almost certain.
Simply because something is improbable, does not mean it is impossible, furthermore the Universe has been around for 14 billion years (and that's just our universe), if we assume that every time a planet formed, the Universe 'rolled a dice' to see if life would occur on that planet, then we look at the number of stars in the sky and assume that each star has, lets go conservative and say each star has only 3 planets on average (which is highly improbable, but not impossible), that is a gargantuan number of rolls of the dice.
To put it in perspective, we estimate approximately 10^20 stars in the universe. That's 10 with 20 0's, or 1,000,000,000,000,000,000,000 stars, which, if our conservative estimate on planets is right, means 3,000,000,000,000,000,000,000 planets, or 3,000,000,000,000,000,000,000 rolls of the dice to see if life would appear.
With that many shots, it's entirely unsurprising that life appeared. Of course we don't know about all the times the roll came up wrong, because we weren't around then. Life might seem miraculous to us at first glance, until you actually do the numbers.
Space is big, bigger than you can possibly imagine, unimaginably big, impossibly unimaginably big. Don't bother trying to imagine how big, you can't, it's just too big.