How's this? (I'm thinking here that the smallest unit would correspond to 1 possible arrangement of the Hubble volume, so the unit would be something like 1/10^70 or something. Any other state of the world is meaningless since it can't exist.)

As usually formulated, Bayesian probability maps beliefs onto the reals between 0 and 1, and so there's no smallest or largest probability. If you act as if there is and violate Cox's theorem, you ought to be Dutch bookable through some set of bets that either split up extremely finely events (eg. a dice with trillions of sides) or aggregated many events. If there is a smallest physical probability, then these Dutch books would be expressible but not implementable (imagine the universe has 10^70 atoms - we can still discuss 'what if the universe had 10^71 atoms?').

This leads to the observed fact that an agent implementing probability with units is Dutch bookable in theory, but you will never observe you or another agent Dutch booking said agent. It's probably also more computationally efficient.