I don't know what infinity over infinity is, but I suspect that it will be undefined.

This. This matters.

Some infinities are bigger than other infinities.

This is more that metaphor. A exponentially larger infinity divided by a small infinity will be infinity. A exponentially small infinity divided by a large infinity will be zero. A division of proportional infinities will be a real number.

So if the chances of a Boltzamann Brain becomes increasingly less likely as enthropy increases. and enthropy increases as time approaches infinity, you have a division of infinities which can equal infinity, a real number, or zero. You won't know which without actually crunching the numbers.