Equipossibility

For example, it is the difference between viewing the possible results of rolling a six sided dice as {1,2,3,4,5,6} rather than {6, not 6}.

This is true even if the die is biased so that 6 and 'not 6' are equally likely to occur (equiprobability).

The Principle of Indifference of Laplace states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying probability distribution.

[2] In Bayesian inference, one definition of equipossibility is "a transformation group which leaves invariant one's state of knowledge".

Equiprobability is then defined by normalizing the Haar measure of this symmetry group.