Make it So
Possible: May or can be; chance
Probable: Likely; more evidence for than against
Plausible: Seemingly worthy of approval or acceptance
When constructing fiction, we're building a world that we want our readers to believe is real. The events that transpire – whether or not they are based on things that "really happened," must be believable to the reader. Our events can be: possible, probable, or plausible.
Probable events are no brainers – everyone accepts that this is a likely, believable scenario or action and there are no flags raised. The reader continues through the situation without doubt. A certain, few number of possible events are allowed, too. If you don't require the reader to accept more than a few possible events, they will have a firm place in your plotting. But what happens when you need to make circumstances that are possible into those that are probable, in order to solidly advance your story?
You make them plausible. How? Like a lawyer building a case, you show evidence, but you do it without too much fanfare. For example, in my current work in process I want someone to die of smallpox. In order to insure that this death isn't too convenient I mention in passing, early in the book, that smallpox has been on the increase in recent years and sneak in a statistic if I can, in dialogue. Some chapters later, I have a minor character die of smallpox – one who really existed and whom my readers could verify if they wanted to. Later, when I kill someone off with smallpox, I have now taken a possibility and made it plausible by building a case. It may initially raise a flag with my readers, but a quick review of the evidence I've quietly marshaled in passing will convince them that it's probable and they will read on, undisturbed.