Meaning of "Volume" : A Probabilistic Approach

"Volume, here, is used in the general sense. It can mean a length on a line, or an area on the plane, or again a volume of space." - Peter Edwin Caines, 2010.01.12

So,
P(Volume= length) ≤ 1/3
P(Volume= area) ≤ 1/3
P(Volume= volume) ≤ 1/3
P(Volume= something else entirely) ≥ 0