Probabilities are easily misused. If I toss a small handful of salt on the table, what are the odds of each particle ending up in the exact positions they do. The predictive odds against it would be a number so large as to be impossible to calculate. Yet there it is! I pick up the salt and repeat, different but yet similarly "impossible" result. Was there a guiding intelligence for that to happen? Am I a miracle worker? Of course not, it was a combination of many factors and forces, all natural. Whats more, now that the handful of sand has been thrown, the actual probability of it ending up exactly as it did was 100% because it happened. And same with the next handful. That is how easily probability can be misused by those with an issue with evolution.
Now If I were to insist upon repeatability of the results, then probability becomes meaningful. My being able to throw the salt and have the results be identical to the first toss would be a miracle, that is unless I was given billions and billions of attempts. Remember, even what seems statistically impossible happens when given sufficient attempts and the outcome isn't prevented by the properties of the salt and table etc.
To continue this illustration, within chemistry and physics there exists a tendency for stasis, IOW elements, objects and forces interact in predictable ways due to the properties of the elements, objects and forces until reactions stop or a new reaction begins that was made possible by the first. There are a limited number of combinations and as a result if we know sufficient details they are fully predictable. Through these inanimate and natural interactions we get complex results, activity, assembly of exotic compounds, wonderfully sophisticated crystalline structures etc. without any outside designer. This predictability greatly alters the statistical probabilities in that among what might be millions of hypothetical combinations in fact there may be only a few possible ones. Even my handful of salt has a limited, albeit large, number of actually possible outcomes. So prohibitive mathematical arguments need to be taken with a grain of salt.
In biology, which is an extension of chemistry, we have the added benefit of accumulation of chance outcomes by means of a selection process. An emergent character of RNA/DNA (and their predecessors) is that errors in the chemistry can be preserved or not dependent of its effect on viability. There have been many computer models of this effect. Random errors are selected through an elimination process and in a stunningly short time what was random takes on a character and appearance of design. Do a google. Anyway, the simplistic statistical analyses of evolution that seem persuasive arguments against it having happened are rooted in a mistaken premise that all theoretical possibilities are equally probable, disregard for time and scale of the early universe and ignoring the selection processes that preserve outcomes that favor the organism.
