One way people of faith recognize God’s involvement in providencial occurances, occurances that unbelievers dismiss as mere improbabilities, is teleological, that events and grouping of events have purpose infused in them. I will again appeal to Maggie’s wonderful sequence as evidence. It is evidence, among other things, of God’s M.O.
This has also been discussed elsewhere:
There is a difference between a set of circumstances that is improbable, and a set of circumstances that is improbable and also performs a function. [emphases added]
And I would include evolutionary events in that as well, evolution being a subset of God’s providence, and why I am an ‘evolutionary providentialist.’