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One can. One starts with the state of zero additional information. This maximizes entropy for 1/6 for each number of the dice. Then one adds the information given and uses the formula for "Bayesian updating" to compute the probability distribution which takes into account that new information.This is a very questionable statement.

What is the probability distribution of something of which the information is given that 5 times someone observed 1, twice 3 was observed, and once 6 was observed? One cannot maximize the entropy given this information. But all information one can gather about aspects of the universe is information of this kind.