There is a probability of <an event> happening <----- Extremely rare , (navi-esque)

 >>>    which is the stronger statement:
-There is a possibility of <an event> happening
-There is a probability of <an event> happening   <----- Extremely rare
                                                             (navi-esque)
if something is probable...  you usu. qualify it ...
                  e.g.
                       more than 1/3 probability that......
                       more probable than not that....
_________________________________
For example:
"There is a possibility of rain tomorrow" is vague and doesn't provide any specific information about the chances of rain.
"There is a 70% probability of rain tomorrow" is much more specific and informative, giving a clear indication of the likelihood.