In Australia, New Zealand, Canada and Britain, and in various European and Commonwealth countries, the constable you're most likely to come across is a police officer of the lowest rank.
Mind you, in Denmark he'll be a soldier, and in the Channel Islands a local politician.
Confusingly, in Britain, at least, a police officer of the highest rant is called a constable too. Between an ordinary constable and a deputy chief constable everyone has different titles (sergeant, inspector, superintendent).
In the USA a constable is also an officer of the law, though not necessarily a policeman.
A constable can also be the man in charge of a royal castle (in which case he may have a rather splendid hat)
Sir Richard Dannatt, Constable of the Tower
and in mediaeval times, in England and France especially, the constable was a the man in charge of the king's army - or he could be the man in charge of conscripting men in his local hundred (an area that could provide a hundred armed men, or perhaps contained about a hundred homesteads),
Of course, if the law bores you, you could always discuss table mats.
In my experience they mostly involve this image:
Flatford Lock, by John Constable, Yale Center for British Art
Word To Use Today: constable. This word comes from the Latin comes stabuli, attendant or count of the stable.
This knowledge will make me look at constables in a new light for ever.