What determines when the ambition penalty triggers?

Solution 1:

After some research, and vigorous testing at the labs, the results are finally in.
TL;DR: Affine was right, you can live in peace and harmony with your ambitious vassals. Presenting some evidence.

• Duke 1 is ambitious, but doesn't want anything from me. There's no penalty. (profile card)
  
• Earl 1 is ambitious and title claimant, but doesn't want anything from me. -50 penalty. (profile card)
  
• Earl 2 is content, but desires one of my duchies. -20 penalty. (profile card)
  
• Duke 2 is content, but wants control of one of my counties. -25 penalty. (profile card)

All of these guys are my direct vassals, and none of them have any inheritable claims to the titles they desire/want control over.

Experiments:

• The reason why Duke 1 doesn't want anything from me, is because I have nothing to give him. He controls the other counties in the duchy directly or through vassals. If I retract a vassal, he will want control of the county (-25) AND the ambitious penalty will appear (-50). He is not a happy camper.
• I created a kingdom title, which de jure holds his duchy. He now wants to become king, and all penalties become active.
• The situation for Earl 1 is a bit complicated. The de jure duchy is outside my realm. He does actually have a -25 opinion penalty to the holder of the duchy for "desires county". Since I can't give him that county, it's a bit unfair of him to hate me so, I feel … unless ...
• This woman is unlanded, but also hates my guts. Like Earl 1 she is ambitious and also a title claimant.

Conclusion:

• Any vassal, content, ambitious or not, may want control of a title. This will trigger a negative opinion modifier of 20-25.
• An ambitious vassal will not automatically have the huge -50 opinion penalty.It will however trigger once you have something he wants, and will then stack with the penalty of "desires/wants to control X".
• Ambitious title claimants will also have the -50 negative opinion modifier.
• Any ambitious character will always have a -5 opinion of any other ambitious character.

This means, that you can have a reasonably good relationship with an ambitious vassal, as long as you keep him happy, and he doesn't have a claim to your titles. Depending on how you structure your realm, this might be feasible. However, once you have something he wants, you might rack up to -80 in negative opinion immediately (-50-25-5). This will make him rebel very fast.

Furthermore, I am almost certain that characters with the ambitious trait are more likely to plot and join factions against their liege.

Tips:

• Avoid ambitious vassals, unless you are prepared to appease them or at least make them vassals of one of your friends.
• Never, ever give landed titles to ambitious people who already have claims to your titles. Not only will they hate your guts, but you will also see the "Count Jimmy for Ireland" factions pop up. In fact, I would perhaps consider invoking tyranny just to relieve them of their lands.