The locations of the spots are defined in the rules, but why are they there and not somewhere else?
Start by understanding that we do NOT play Snooker on a Snooker table, we play Snooker on an English Billiards table and the spots are placed for English Billiards players.
The layout for a full size table was a collaboration between John Thurston and the first actual billiards champion one Jonathan ( Edwin) Kentfield in the 1830’s.
The Baulk Line for English Billiards (hence Snooker) at 29 ins. allows a perfect half ball angle for the losing hazard (in-off) from the pyramid spot (Pink) into the top corner pocket with the cue ball set at either end of the 23ins.
The Pink (Pyramid) Spot and the Blue (Centre) Spots are fairly obvious.
The Spot (Black) is on the centre line of the table, twelve and three-quarter inches from the face of the Top cushion, in exactly the right place that allows a perfect half ball angle for the losing hazard (in-off) into the top corner pocket with the cue ball set at the drop of the centre pocket .
The markings on the table are derived mathematically, based on the distances between the faces of the cushions, so if you have a non-standard table size, you should be able to determine them.
Here is a diagram:- L=Length & W=Width
Use a string drawn taught between the centre of the fall of the corner pockets in an ‘X’ shape to find the Blue spot.
Similarly, string drawn taught between the corner pockets and the side pockets will find the Pink spot