Leica, Nikon (and Canon) rangefinder use 51.6mm as their standard focal length. Contax uses 52.3mm.
Very early Jupiter lenses (up to 1952/53 or so) used the Leica standard and then switched to the Contax standard. Which means that a younger good Jupiter lens is either (1) out of focus at close focus (around 6 inches at 1m) and accurate at infinity, or (2) accurate at close focus and soft at infinity, or (3) somewhere in between. Brian used to adjust later Jupiter lenses via shims to (2).
If you want to use a Jupiter 3 on your Canon P, you can either live with (2), or buy an LTM copy from 1952 or older (typically they have Zeiss glass, and/or are marked as ZK), or buy a Contax mount lens with a Contax Helicoid adapter as sold by Amadeo.
Note that there is an additional problem of large manufacturing tolerance, basket cases, etc., as Boris stated above.
I had several copies. The one that performed best was a ZK copy.
That being said they are not so cheap anymore, and even a well adjusted lens is still cheaply built out of aluminum, etc. If you like the signature, you might consider looking for other lenses with similar design, as for example Canon 50/1.5 or Nikkor 50/1.4, both the same Sonnar design, biut heavily brass and chrome built and all around fun to use. Like this:
Good luck,
Roland.