If there is a finite probability of something happening (ie. a planet forming around a star, or a galaxy forming), then in an infinite universe there will be an infinite number of that thing.In this sentence, the word "finite" has to be read as "non-zero" to make any sense. Finite means not infinite. He is confusing zero with infinite.
Likewise, the term "finite chance" is always misused. The terms "slim chance" and "fat chance" are also confusing. You would think that these terms would be opposites.