"Finite chance", or "finite probability".
All probabilities are finite; the possible range is 0 to 1, inclusive.
As used, the phrase seems to be intended to mean "nonzero probability", which is not at all the same thing. Zero, after all, is eminently finite.
Just another case of colloquial usage and mathematical usage not lining up at all. (See also: "lowest common denominator".)
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