An isotropic probability distribution means that the probability of all possible outcomes is identical. For example, games of chance often use a device that has an isotropic probability distribution, at least in theory. A six-sided dice has six possible outcomes, all of which are supposed to be equally probable and with no discernable statistical variation even after accumulating statistics over a trillion rolls. Note that this is also the definition of "random".
The problem with this assumption is that even good "random" number generators have subtle anisotropies that we get better at detecting every year, and just about every real system has gross anisotropies in outcome probability that are quite evident. The cumulative odds change dramatically when playing with a loaded dice.
It's even deeper than that. No uniform probablity distribution exists for the whole line (or plane, etc.). Nor does a uniform distribution exist on the integers. Otherwise, if challenged to "pick a number" one would usually pick a number that takes longer than the age of the universe to write down.