As mentioned, there are a lot of specifics to get that authentic Ric tone. However, you can get a tonality that can get pretty close with proper pickup locations.
To get that Ric bridge pickup to sound Ric-ish, it needs to be located in the Ric bridge pickup spot, which would be centered about 29 7/8" from the nut on the bass (assuming 34" scale). This is where the harmonic rings at the '36th fret.'
The catch is that location would have the pickup butted right up to the P bass pickup, yet it would still be pushed towards the bridge a bit. Well, now you somewhat have the bridge tone, but that fatter, deep fundamental Ric neck tone is not right at all with that lower mid sounding P bass pickup in it's current location. Here's a photo showing Ric vs J bass pickup locations. It would be easier to put pickups on a J as the J neck pickup isn't a wide as the split coil P pickup and the J pickup is located a touch closer to the neck vs a P pickup. The P pickup neck side coil is at about 28" from the nut, the J pickup is at 27.75".
You can more closely fake a Ric sound with single coil J bass pickups in the proper spots vs Ric pickups in the wrong spots. To do this right, put one pickup at that '36th fret' location, the other at the '24th fret' location. This would require a LOT of cutting, routing, etc... on your beast. You may or may not want to make that sacrifice. You can pretty easily convert a cheap P bass to a Ric tone clone. The pickup routs are all done in the part of the body covered by the pickguard, so you can get a blank P bass pickguard, then make some crude routs on the body for a variety of pickups and do cleaner cuts for the pickups on the pickguard to cover up the routs to the body. This can also be done on a J bass, but the P bass not having a bridge pickup already routed into the body would result in a cleaner looking final product.
I made my Ric sounding bass on the cheap by using a Peavey Patriot as the platform. It's single Super Ferrite pickup is in the Ric spot, and by adding another in the proper neck location, I ended up with a bass that pretty much nails the Ric tone for $300. Bonus is that Peavey Patriots are a much nicer bass than their price would lead you to believe and the Super Ferrite is an amazing pickup. See this thread that discusses ways to fake a Ric tone. My Patriot is post #63 (page 4) in the thread.
Rickenbacker pickups on a precision?