Authority is almost always used to describe argumentation based on sources other than logic or evidence.

The right kind of authority is based on logic and evidence. Most of most people' beliefs have not been personally verified by them. You probably havent' personally proven probability theory from scratch

Authority is practically meaningless as a concept if it includes both accurate and inaccurate foundations of argumentation

Fortunately, English allows us to qualify nouns with adjectives. Which allows us to distinguish between X-ish and Y-ish authorities.

. Probability theory works, appeals to authority don't.

Probability allows you to do things with clearly defined idea and evidence. Getting them clearly defined is the underwater part of the iceberg. That probability theory doens't help with.