Why does "to keep someone posted" mean "to keep someone updated"?

According to Etymonline:

Posted, meaning "supplied with news," 1828, American English, past-participle adjective from post (v.2).

Here is the second entry for the verb 'post':

in bookkeeping, "to transfer from a day book to a formal account," 1620s, from post (n.2) via a figurative sense of "carrying" by post horses.

Here is the second entry for the noun 'post':

"place when on duty," 1590s, from Middle French poste "place where one is stationed," also, "station for post horses" (16c.), from Italian posto "post, station," from Vulgar Latin *postum, from Latin positum, neuter past participle of ponere "to place, to put" (see position (n.)). Earliest sense in English was military; meaning "job, position" is attested 1690s.