The game rules chattily assure you that the murder did not take place in the Lab, on the Table, or by the Detector…but of course this is simply disinformation coming from a source that you are likely to erroneously assume is authoritative, even though you have no firm evidence that the rulebook is a reliable narrator.
If you did design this game,
...should be in the rulebook.
Agreed. Especially since not everyone will read the rulebook. Usually one person learns the rules and tells the other players.