The chance is 1/7,000,000,000
There is, seemingly, a 50/50 chance he will die, due to the fact that, related to him, there are only two outcomes, but the act of pushing the button is the event that you use. Since the button kills one person in the world, and there are roughly 7 billion people on Earth, the chance is 1 death out of 7 billion possible deaths.
If you were pushing a button that would either kill your friend or not kill your friend, then the chance would be 50/50, there being only two outcomes. However, the button has 7 billion outcomes as opposed to two.