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> “I went to THE post office”, “I went to THE train station”.

In my hometown: There's only 1 of each and wouldn't be confusing.

Where I live now: Which one?

These don't refute GP's definition, your examples are just missing the shared context that determines whether it's correct or not.

I think definiteness doesn't need to be a shared context.

"I went to the the train station to pick up a map on my way here". "Great, thanks!"

It was a specific train station that I chose intentionally or visit regularly, but it's not relevant to the conversation which one.

If I were to use "a train station" then it implies I didn't care which train station it was.