You know that moment when you realize that something in your plot is entirely dependent on coincidence? And you think that the reader might scoff because it's so unlikely? And the event is too important to the plot to drop or change radically?
Well. You know, acknowledging this problem is the first step to fixing it. The next step is to explore how it COULD happen if it can't happen coincidentally.
Whenever you find yourself saying, "Just happened to-- So Pete just happened to stop by the restaurant for dinner..." assume that you're trying to do an end run around plausibility. Stop. Think through.
Let's start with an example. Coincidence is pretty common in mysteries, especially classical mysteries (like Poirot), because you need suspects. That is, in this location, you need a whole group of people who had motive to murder the victim.
Here's one I just encountered.
Heroine and heroine are at a country inn in England (this is in the 19th Century). A decade ago, the heroine left her home in Russia. Now at the inn, she encounters a Russian man who worked for her parents. That night, he's murdered. Oh, and I need some suspects, besides her, right? So here's the Foreign Office official who was posted to Russia back a decade ago, and the mysterious Frenchman, a former soldier who was on Napoleon's ill-fated march to Moscow, and....
But the biggest coincidence is simply that someone in England runs into this Russian guy and cares enough to murder him.
So first step is accepting there's a problem, that this is too big a coincidence. As soon as I realized that, I admitted also that I did need for things to transpire pretty much this way-- the Russian has to accost her at the inn, the other suspects knew him and were also at the inn. So I spent a bit of time thinking how could that be so?
Well, because everyone planned it. I think the Russian was trying to blackmail the couple, and so he sought them out in London. The Frenchman is hanging out with a bunch of emigres in London (he's just a red herring, so he doesn't actually have to know the Russian at any point, as he didn't actually kill him or seek him out. He's just foreign, which is suspicious.) The Russian was following her (to give her something of her father's), and Foreign Office couple (suspecting he knew something about their nefarious activities in Russia, and no, I don't know yet what they are :) followed him to the inn, and so did the Frenchman. So there's only a bit of coincidence at the beginning, but after that, everything's planned. But of course the murderer wants it all to seem like coincidence ("I just happened to be passing by...") so there would seem to be no motive. I will doubtlessly refine as I write, now that I accept that there's too much coincidence. And I'll emphasize things like... oh, London is a big city, so it's not as unlikely that foreigners would be there as in a remote country inn. And I'd imply that these were not invisible people (they were rich and well-connected) so they'd be easy for the Russian to find if he wants to track them down.
Anyway, it's hard to acknowledge that too much of our plot relies on coincidence. But acknowledging that is really the first step to remedying it. And all you have to do is think, "If this same thing happened because someone made it happen, how would it happen?"
I do have to point out one problem that comes up, however! I had a book where I had a seeming coincidence in the opening. It wasn't a coincidence, actually-- that was just a clue that the man knew the main character in the distant past. But when I sent the first three chapters to an agent, she rejected it, saying that the plot relied too much on coincidence. But it didn't, I wanted to protest. It just seems like coincidence, but all makes sense later! But it was too late. (And that might only have been the ostensible reason for rejection anyway.) So I'm not sure how to hint that it's only LOOKS like coincidence. Thoughts here? What about in the query letter? What about in the scene of seeming coincidence itself?