1 for every single person you care about to the total world population, reduce as possible.
For the sake of the argument, let's say the people you really, really don't want to die total, and I'm just picking an easy number here, 50. Let's guesstimate about 7 billion people besides you with beating hearts on this planet. 50/7,000,000,000. Reduce, we get 1/140,000,000.
Those are the odds that pressing the button will kill a loved one. However, if we word it just a little bit differently, things get confusing. Instead of "what are the odds the random person will be a loved one?" we say "this button will either kill a loved one, or it won't." The difference is the complete disregard for probability.
Personally, I like them odds.