But that requires considering the three hypotheses as a group rather than in isolation from all other hypotheses to calculate 0.33.

Not really. A hypothesis's prior probability comes from the total of all of your knowledge; in order to determine that P(HA)=0.33 Lumifer needed the additional facts that there were three possibilities that were all equally likely.

It works just as well if I say that my prior is P(HA)=0.5, without any exhaustive enumeration of the other possibilities. Then evidence E confirms HA if P(HA|E)>P(HA).

(One should be suspicious that my prior probability assessment is a good one if I haven't accounted for all the probability mass, but the mechanisms still work.)