I'm ... concerned since in my case the "idea" is rather a specific one: In Irwin Blye's Secrets of a Private Eye, a kind of manual on the methodology of private detectives, he mentions in passing a female client who insisted upon his wearing a trench coat whenever they met, even though this was not standard practice for him.
You're fine. Generally, two types of borrowing constitute plagiarism:
1. Uncited direct quotations (including those that have had a word or two switched around)
2. Sequences of ideas supporting a point
#2 is applicable to nonfiction. It essentially means that you can't go look at someone's journal article, copy his logic, and write a book on the same topic using the same argument without citing him. Endlessly derivative plots in fiction are fine. If I were you, I would write a preface acknowledging any significant influences, but I wouldn't worry about unintentional plagiarism unless you find yourself accidentally copying the actual text of someone else's work. (It is possible to do this from memory. I've caught myself accidentally doing it in papers on a couple of occasions. Luckily, I noticed in time and was able to put in citations.)
If you want a
readable guide to plagiarism, take a look at academic honesty codes. Most universities have lots of webspace devoted to the subject. A real case on a relevant topic is the controversy over Frozen and Dorothy Lewis. (
http://en.wikipedia.org/wiki/Frozen_(play)) Notice that Frozen borrows much more from Lewis' work and real life than your one puny little idea. The references were of a type where people other than Lewis and the playwright were able to easily recognize their source--yours isn't.
Also remember that plagiarism and copyright infringement are totally different concepts. An act can easily be one or the other or both. You cannot copyright ideas, but ideas are often plagiarised. You are not plagiarising if you cite, but you may be using more text than you're allowed under fair use, which would mean you're violating someone's copyright.
The bottom line: you are borrowing a single
real event for a work of fiction. It's not plagiarism, it's not copyright infringement, and it's not the type of thing Blye would be able to sue you for emotional damages over. Stop worrying.