There are 3 main different conceptions of probability in the literature. One that I don't find very intuitive but that is widely used to explain this type of case is the Popperian one. According to this view, 1/1137 means that when you push the occurrences of something into infinity, on average, event X happens that many times (a more typical example is that when u flip a coin an infinite amount of times, tails/heads p = 0.5/0.5)
PSO doesn't have a pity system, that is, you're not guaranteed to get an item after you kill n amount of monsters. As such, you may get the item sooner or later. 1/1137 is just what should typically happen. But what should typically happen doesn't always happen.
TL;DR 1/1137 does not mean you are getting an item after killing a monster 1137 times. You may get it later or sooner. It's a bit unfortunate that you didn't get it yet but it is what it is.