So, you're taking the frequentist approach, the probability is the fraction of the times the event happened as n goes to infinity? But tomorrow is unique. It will never repeat again -- n is always equal to 1.
And, as mentioned in another reply, calibration and probability are different things.
But tomorrow is unique. It will never repeat again -- n is always equal to 1.
The prediction is not unique. I group predictions (with some binning of similar-enough predictions), not days. Then if I've seen enough past predictions to be justified that they're well calibrated, I can use the predicted probability as my subjective probability (or a factor of it).
Alternatively, what single concept from statistics would most improve people's interpretations of popular news and daily life events?