Cannon, not canon (the official texts, e.g. biblical canon, or Star Wars canon).
They don't launch space probes out of cannons because they don't make it out of the atmosphere. According to [1], muzzle velocity of a cannon is about 1685 ft/sec, which is 0.51 km/s. Delta-v to orbit is around 10 km/s. This is a feature, though, because launching your cannon shell into orbit means it isn't hitting it's target.
But let's suppose you have some propellant that is 20 times more potent. A cannon imparts all the energy at the beginning, with the acceleration happening as the expanding gasses push the projectile out of the tube. Assuming that the probe survives the initial explosion (unlikely), it is going to accelerate to 10 km/s very rapidly. Once calculation [2] put the g-force on a cannon shell to be 15 g, but lets say 10 g to be conservative. So we need 20 times more acceleration, so 200 g. Even if your probe is not smooshed in the acceleration, it is unlikely to be functional. (Note that, in comparison to cannons, rockets avoid this problem by providing the acceleration over a long period of time)
Now if you managed to engineer it for 200 g, air friction is going to burn it up. We know this because when spacecraft come down they have to lose all the velocity they got going up, and they tend to burn up. Heat shielding is almost certainly going to put you over the weight limit.
What, you say? This is a space cannon? Okay, well leaving aside how this cannon is going to burn the propellant without oxygen, the delta-v to Pluto from LEO is 8.2 km/s, so Sedna will be a little bit more. This is still an order of magnitude larger than the cannon, and still has acceleration problems. Plus, you had to use a rocket to get the payload to the cannon, so putting a second stage on the rocket.
You still have the issue that it's going to take a couple of decades to get there, which is what this paper is trying to address.
[1] https://www.arc.id.au/CannonBallistics.html
[2] https://math.stackexchange.com/questions/3249185/calculate-g...