It would depend mainly on how the length was selected... If it was selected uniformly and randomly then it could be described as "random length" and we could speak in terms of the probability of selecting that particular length. But if the length was predetermined before cutting the wire, and hence no longer a randomly selected value then the probability of selecting that particular length would be 1.
A random variable is a mapping of a sample space to some value (usually, but not necessarily, a real value). So, for example, in terms of wire length if a sample space includes a continuous set of values between 50-100 feet and X is a random variable on that space we can use X as a value, i.e (X <= 75 ) if we are speaking in terms of probabilities of X i.e. Pr(X<= 75).
With respect to ham radio and "random antennas" its more an issue of semantics than precise mathematical definition. So in amateur/SWL lingo "random antenna" refers to any antenna that is not necessarily mathematically related to the exact wavelength(s) in use. Or, so they say.
I would say it is an oxymoron depending on how the actual legth was selected, i.e. randomly or predetermined.