I think that arguing for ID by referring to the mathematical probability of a past event occuring makes no sense. It misapprehends both probability and evolution, and fails to take into account the inherent observational bias the we experience based on our place in the universe.
It is inherently erroneous to talk about the probability of any past event happening. The probability that a past true event happened is 1 (or if you prefer 100%). Before the event happened there may have been some probability attached to the event, or it may have been compelled as certain because of factors that were not apparent to the observer. But you can’t put a probability on a past event.
This is not mere semantics. Take this example. If I write numbers from 1-1,000,000 on little slips of paper and toss them into the air, what is the chance that I will randomly grab number 12 as they float past? If I try to grab 12 and succeed, that would be remarkable. But if I grab randomly and get 12, I wouldn’t declare 12 God’s will, or say that grabbing 12 is evidence of God’s design. Its just the number I happened to get. It doesn’t make 12 more or less special. Once I have 12 the chance that I have 12 is 1, not 0.000001. It is unremarkable.
To say that it is remarkable that this particular planet developed an atmosphere similarly misapplies probability. It looks at the issue from the wrong side. What is the chance that the planet we live on would have a atmosphere? It is 1, because we could not have developed as we are on another planet. The fact that this planet out of the billions and billions of planets is that one is no more remarkable than the fact the 12 was the number grabbed. It means nothing.
I hope this is not terribly confusing, because it is an important concept in this context. Our observational bias, combined with a misapplication of the probability of future events onto the past creates an impression of design, but it does not in any way prove design.
This gets also to the problem of the God of the Gaps. I believe that in this world-view God is reduced to a force that explains gaps perceived to be created by supposedly improbable past events. But probability is only gauged by the viewpoint of the observer. Some day we may be able to model air currents and bits of paper sufficiently to predict that I would have grabbed number 12. Some day we may learn that these supposedly random past events were forced by rules we don’t understand now. Each time that happens another gap will close. When all the gaps are closed, what happens to the God of the Gaps?