Logically, these two are worlds apart.
Their roles in argument are vastly different. Probability is the realm of statistics and quantitative studies. Probability is concerned with frequency of occurrence. Possibility is more the realm of the qualitative; it is concerned only with whether or not something has occurred.
While I know that quantitative studies are somewhat more prestigious, I think that a qualitative study which understands that the role of qualitative work is to explore possibility, can be equally profound and equally logically defensible.
But I think they also play an important role in our lives and in managing a large project. We cannot get lost thinking about probabilities; we must keep an eye on possibilities as well. Looking at probabilities leads to living a life of undue caution--to the point, possibly, of paralysis. Looking at possibilities without consideration of probabilities would lead to a naive view of the world. We need to balance the dream with prudent caution. For the writer this means that we have to balance the dream of our work being accepted with the likelihood of its being rejected. We have to chase the dream in the face of the danger--and in order to do that we must put pen to paper (or finger to keyboard). In order to finish a big project we have to dream of the big project being completed, and then persevere when circumstances argue that the probability of completion is low. But we always want to be sensitive to all the choices that we can make that affect our chance of reaching our goals. (And in that context, a dissertation writer might do well to remember that completing the dissertation is one thing, and writing a book for publication is another, and no matter how wonderful you want your dissertation to be, you can choose to hold yourself to a lower standard than a dissertation that is publication ready.)
Imagine the possibility of finishing your writing project. And then write it!