How is an air accident's probable cause determined?
I participated in a tiny supporting role in a few crash investigations involving CRJs, so I'll give it a shot, and I would say that when a main cause is listed, especially for something mechanical, it's what you might call a "primary trigger", without which, follow-on supporting factors  and events that led to the crash would never have occurred.  Or an event in a chain that can be considered the "point of no return".

Pilot with poor training takes off in an overloaded airplane, and engine quits after V1/VR and it crashes.  The engine failure will be the main cause, with poor training and overloading added as contributing factors.  Without the engine failure, the poorly trained pilot in his overloaded airplane would've carried on his merry way, so the engine failure can be considered the main cause.

For pure "pilot error" events, it can be more nuanced, with a roughly equal-in-impact chain of events and if you took out any element in the chain, the other elements may have still happened, but just not leading to a fatality.  These reports will often list a series of accident causes without giving critical weight to any one, except to say that the cause was ultimately the crew and not the plane.  Running out of gas is a typical one.

On the other hand, sometimes a crew action is as much a triggering event as a major mechanical failure.  Colgan Flight 3407 is a classic example of this.  The Capt had the Mother of All Brain Farts and pulled when he should have pushed when the shaker went off and this is listed at the main cause.  Now, the shaker went off in the first place because they weren't paying attention to power when the A/P leveled off, but it was the response to the shaker that sealed their fate, and becomes the main cause.  

There was a CRJ crash in China caused by taking off with frost on the wings on a cold clear morning.  Frost on the wings was the main cause.  Lack of understanding of the effects of frost, and maybe a bit of normally benign over-rotation-on-takeoff contributed, but without the frost, nothing would have happened.