How does Halfling Luck affect the probability of surviving my death saves?

The probability of a mere human surviving a series of unmodified death saving throws has been established as 59.5125%. But Halfling Luck applies to death saving throws in a dramatic way: A roll of 1 on a death save normally counts as two failures, but halflings are much less likely to suffer this result.

Previous work in the field of calculating the effects of Halfling Luck does not apply directly to death saving throws, because of this asymmetry between races concerning how terrible it is to roll a 1.

How much more likely is it that a halfling will survive a series of death saving throws as opposed to one of those poor unfortunate nonhalflings?