Well Curious, no it does not deny the existence of God because it does not mention God. It is a scientific examination of certain processes. Instructions about putting together a tv cabinet do not deny the existence of clothes either. They are simply not mentioned because they are moot to point.

And in answer to your question about probability. The rate of probability is low, yes. But in realistic terms means it can happen often. For example the probability to win lotto might be 1 in 20 million, which is a fairly low probability. Say that half of America decided to play the lotto. That makes 6 or 7 people who actually won. Probability doesn't mean it's unlikely that something is going to happen, it means that something WILL happen, but only once in a certain amount of tries. For the lotto example, it means that that the lotto WILL be won, but means that YOU will be unlikely to win it.
And when we talk about evolution and particles and bacteria etc. We're talking about a number that human minds can literally not comprehend.