The phrase "a possibility of falling" is correct and usable in written English.
It can be used when discussing the likelihood or chance of experiencing a fall, whether in a literal or metaphorical sense.
Example: "When hiking on steep terrain, there is always a possibility of falling, so it's important to stay alert."
Alternatives: "a chance of falling" or "the risk of falling".
The organisation is reviewing the rule following the Dwain Chambers court challenge and there was a possibility of falling in line with the IOC's new rule under which an athlete banned for six months or more misses the Olympics after their suspension finishes.
If they withdraw now there is a possibility of falling Afghanistan back into during the Taliban regime," Nawandish said through an interpreter.
There is also a possibility of falling dust being transported in the air from large industrial regions, such as Bratislava, Vienna, Budapest, or factories near the Nitra district.
Light is the enemy if you think there is even a remote possibility of falling back asleep.
There was a certain wistfulness in Armstrong's tone as he read from RM Ballantyne: "Boys ought never to decline to climb a tree to pull fruit merely because there is a possibility of them falling off and breaking their necks".
The National Sleep Foundation also cautions that a lack of sleep creates the possibility of falling into a 3-4 second microsleep without realizing it.
They have been replaced by an anxiety about the possibility of falling out of their economic class".
A few months ago, the possibility of falling into the abyss seemed all too real.
In the 1980's, early in the shuttle program, the possibility of falling foam striking an orbiter during launching had been classified as "Criticality 1," a problem that could cause the loss of the spacecraft or its crew.
The gap maybe caused by the immersion in electrolyte and repeated charge and discharge cycles that proved after a long period of cycles, electrode material has the possibility of falling off from the copper foil, but it was still much better than PVDF binder.
Part of Eighth Avenue was shut down, with officials concerned about both the stability of the rig and the possibility of falling glass when firefighters cut through a window.
