When trying to connect to an external postgres database using pgAdmin, I get an error
The cause of the is the bold part, the host "":


  "FATAL: no pg_hba.conf entry for host "", user "postgres", database "postgres", SSL off"


The database, from which you get the error, see a local connection, and not a networked one.

How can it happen, it depends on your system configuration, what you didn't share here.