Mathematically explainable or higher Providence?

I don't believe in coincidence and fate, as a technician I am used to the formulas of probability. Why coincidence? ... I don't deny it was more than just a coincidence that everything came this way. It was a chain of coincidences. But why do we have coincidence? I don't need any mysticism to accept the unlikely as an explanatory fact. Mathematics is enough for me!  ( Walter F. in "Homo Faber")

I can well imagine that many a well-educated contemporary can be found in this quotation. This or something similar has often been argued to me, especially by people with a scientific influence.
   But let's be honest: isn't it a little small-minded to want to explain extraordinary coincidences purely mathematically? According to the motto: Statistically speaking, the unlikely event has to happen at some point. So there is no need for higher steering as an explanation!

So let's assume that this would really work with a mathematical explanation for improbable events (- personally I doubt it -), then this wouldn't necessarily mean that higher powers couldn't have intervened in a controlling way, would it?
    In all honesty, this cannot be categorically excluded. It should at least be recognised as a possible explanatory model.
    Personally, however, I think that on closer examination one gets enough circumstantial material to be able to assume a higher control in the so-called extraordinary coincidences of life. I will try to support this thesis in the following parts.

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