For now, it seems that the majority of ambitions are on two paths:
Parabola is practically guaranteed to be incorporated with the ambitions, the only place where Clara’s baby can be born (Light Fingers), where the cards and the venue can be acquired (Hearts’ Desire) and the only place where the bomb can be detonated (Bag a Legend) and as for Nemesis, well I’m not really sure about Nemesis.
B. A confrontation with a Master
With the exception of Light Fingers (correct me if I’m wrong about that) every ambition includes a Master in some key way. Which likely means that they will confront them, most likely about the nature of the ambition, and possibly how the Masters created it.
The reason that they would do this is pretty simple, after all, why do the Master’s do anything? As the Duchess says, "In the deepest matters of the Bazaar, always look to love". In creating each ambition they created a brilliant love story. Nemesis is the haunting tale of someone who became a monster after they lost their loved one. Heart’s Desire is about someone who blackmailed, deceived and manipulated his way as well as possibly sacrificing his very soul in order to attain his heart’s desire. Bag a Legend is different, as it is arranged by Mr. Veils (The Vake simply wants to hunt down people in Parabola for fun). Light Fingers is the only one I can think of that isn’t (to my knowledge) directly affected by a Master.
To summarize, my theory is that the ambitions are arranged by the Masters to lure players into Parabola and to manufacture love stories (two birds with one stone).