  We introduce a novel notion of probability within quantum history theories
and give a Gleasonesque proof for these assignments. This involves introducing
a tentative novel axiom of probability. We also discuss how we are to interpret
these generalised probabilities as partially ordered notions of preference and
we introduce a tentative generalised notion of Shannon entropy. A Bayesian
approach to probability theory is adopted throughout, thus the axioms we use
will be minimal criteria of rationality rather than ad hoc mathematical axioms.
