When we examine the data, it turns out that celebrity deaths are actually just a normal part of life - they don't really come in threes at all. In fact, studies have shown that the law of averages dictates that, given the large number of famous people in the world, it's actually likely that two or three will die within a short period of time.
But here's the thing: our brains are wired to recognize patterns, even when they don't really exist. So when we hear about a few celebrity deaths in a row, our minds start to make connections and think, "Ah ha! It's happening again - they're dying in threes!"