It's a good point that the answers are still being looked for.
Question: How do you mean improbable? I would differentiate between an improbable event and an improbable fluctuation within a process.

@ErgodicMage well evolution doesn't necessarily exclude God, and it doesn't include the origin of life either, but neither would the origin of Life have been formed from organic matter. But when you push evolution as far back as to when life began , or how the universe began,these are things that we don't know nearly as much about.and if you push back far enough you'll eventually get to something that no one knows. But our not knowing what made life come alive does not change the verifiable fact that life does evolve and certainly has evolved.

@Ritchie
I generally don't invoke any god into a scientific discussion (though I will invoke science into a god discussion), my 3 reasons are:

1. it usually leads to biases that leads away from understanding.
2. it introduces an independent variable into the domain without necessarily adding to an explanation.
3. it's too easy to fall into a "God of the Gaps" thinking. I went down that path before and it didn't work out well.

I'm not very knowledgeable about abiogenisis, but from what I know it can basically be explained through natural processes. There are parts that are not understood as yet, which I take to mean that more work is needed for better understanding.
I previously noted a difference between an improbably event (I should have added external) and an improbable fluctuation within a process. An fluctuation or event within a process still leaves a natural process that can likely be explained by natural means.

"But our not knowing what made life come alive does not change the verifiable fact that life does evolve and certainly has evolved."
Yes, Evolutionary Theory has done a good job of explaining how life has evolved, from what I understand it even holds up well with newer knowledge from DNA. There are some things that still need to understood though. IIRC there is uncertainty in how the causal relationships between natural environment and DNA changes, what is the mechanism that brings the relationship together.

@ErgodicMage Abiogenesis has a decent amount of evidence behind it but nowhere near as much as evolution does.so far we still don't know which or how many are the current competing hypotheses posed for the origin of life or most accurate. I'm going to try to answer your question accurately, mutations can cause instant adaptations while natural selection is the process by which adaptations occurs over a series of generations. Adaptations or changes or processes of changes by which an organism or species becomes better suited for its environment.a mutation is an altercation of the DNA sequence.

Glad to be here!