"most likely possibility" is correct and usable in written English.
You can use it when you want to refer to a situation that has the highest probability of occurring. For example, "The most likely possibility is that the weather will stay sunny tomorrow."
"But it sounds like that is not the most likely possibility".
Or, in perhaps the most likely possibility, they could have him begin the season in a Mets uniform.
If the Mets move Wigginton for a pitcher -- Pittsburgh's Kris Benson is the most likely possibility -- they run a significant risk.
The most likely possibility is that the Ryder Cup will be played Sept. 27-29 , 2002 the week after next year's American Express Championship in Ireland.
The most likely possibility is that the government will spend more on health care today, promise to realize savings tomorrow and never succeed in lowering costs.
In what some consider the most likely possibility, the creditors would agree to renegotiate the terms of the bailout and the new Greek government would go along.
Among the most likely possibilities: asylum, because they fear persecution in their home country, or a special immigrant juvenile status for children abused or abandoned by a parent.
The two most likely possibilities are a landslide or a mud volcano, Yeats told LiveScience's OurAmazingPlanet.
Lewis said the most likely possibilities were Kenyanthropus platyops (fossils of which have been found nearby) or Australopithecus afarensis (the species famously associated with the fossil known as "Lucy").
When enabled with the permissive option, the most-likely possibilities will all be included.
Most likely, the possibility of being called before the House Un-American Activities Committee played a role.
