«Salle» used in a general sense mostly refers to a 'large room' (grand hall or similar), or is used for specific rooms eg salle de bain, salle à manger, salle de classe. «Pièce/s» is used to refer generally to a room, or the number of rooms in a house/apartment etc. «Chambre» is usually applied to a bedroom in residential use, hotel or hospital rooms (which are basically 'bedrooms'). I don't know of an expression '10th clown in a room' either in English or French (it is certainly not an expression locally), but I would use «pièce» for room here as my first choice. If it is a fixed expression, it may take another form.