The other problem is that these definitions are time independent - they treat the probability of each event as a roll of die, when in fact each previous event i

The other problem is that these definitions are time independent - they treat the probability of each event as a roll of die, when in fact each previous event impacts the probability of future events, by impacting surface features, moving centres of production, driving further energy expenditure and altering haloclines and other such variables. It's a positive feedback process.