Looking for a translation of a German expression "mit an Sicherheit grenzender Wahrscheinlichkeit"

You might just go with the literal translation with probability bordering on certainty, which doesn't sound clunky at all. It actually sounds quite witty in English with exactly the same nod to mathematical sophistication.

As an alternative, you might use with confidence bordering on certainty.

Roger Ebert uses "with a confidence bordering on certainty" in this review of a film.

Actually, a google search of this latter phrase shows a lot of hits.

Certainty can be modified by moral (or certain by morally) to indicate a degree of certainty short of absolute. Thus to a moral certainty might well do as an idiomatic translation of mit an Sicherheit grenzender Wahrscheinlichkeit.

OED s.v. moral:

7. Of evidence, argument, etc.: based on a knowledge of the general tendencies of human nature, or of a particular person’s character; probable rather than demonstrative, sufficient to justify practical certainty. Of a belief: held as practically certain. Freq. in moral certainty n. a degree of probability so great as to admit of no reasonable doubt; a practical certainty on the basis of moral evidence.

In some fairly early usage, e.g., George Campbell’s Philosophy of Rhetoric (1776) Chap. 5, this means any degree of certainty falling short of the absolute certainty of mathematical or logical proof or demonstration, including the by-word certainties of death and taxes and the strongest evidences of our senses and physical sciences concerning the world around us; but the definition offered by the American Heritage Dictionary (again, s.v. moral) suggests a degree of certainty considerably less than those:

6. Based on strong likelihood or firm conviction, rather than on the actual evidence: a moral certainty.

Ngram shows these phrases declining in frequency since the all-time high associated with Campbell’s publication, but still current though a little recherché, as (we are told) is the German expression in question.