I once read or heard somewhere that the biggest problem self published authors face is anonymity not someone stealing your work. If I had to choose between the two, I would choose anonymity because the thought of someone stealing my work is terrible. And fair warning now, if anyone steals my work I will hunt them down.
But that doesn’t mean that you are safe. There are many examples of people stealing other author’s works and posting it online as their own. Often the only time they are caught out is when the fans of the real author catch on to what is happening. Some examples are Shey Stahl who is accused of stealing a twilight fan fiction story and Kay Manning who has stolen multiple stories from multiple authors. Both people used Amazon and/or Smashwords to sell their books. Or this post that talks about an Argentinian politician drafting anti-plagiarism using plagiarised material from Wikipedia.
Before you think that the only way you can find out if that story you wrote was plagiarised is to wait for a random reader to stumble across it, then think again. This website, while it helps improve your writing also scans for plagiarism. Grammarly allows for chunks of text to be submitted and examined to see how plagiarised and grammarly incorrect your text sample is.
Also if you have any extra info about how to detect plagiarism feel free to list it in the comment section below.