What you search seems to be a mix of GIS software and maybe something like Google map.
In any way, if you want to calculate distance on your map, you need to georeference it (ie associate local coordinates (pixels) with geographic coordinates.
In your case, it's quite simple because for a global map coordinates are :
left bottom : -90 ; 180
left top : 90 ; 180
right bottom : -90 ; -180
right top : 90 ; -180
For this you can use software like Quantum GIS and you can begin with tuto like this one.
Is it what you are searching for ?