We'll start off with the television. If you asked someone two hundred years ago how electricity worked, they'd look at you funny, since electricity itself was a brand new thing.
Magic, and Leaguer and I have had this arguement just recently, comes down to one simple rule each and every time. It has to create something from nothing, which violates a simple law of the universe, as we haven't been able to develop a situation where something goes away forever. This is WHERE Quantum mechanics comes in. The rules of a television don't violate things. Electricity powers the television, and the television reflects the energy in it's own way. Anybody who has basic understanding of energy would see this.
Quantum probability has very little to do with it, as it basically just states that one band separates into two at a junction, rather than a merging of a reverse function. Basically different dimensions for different reasons. And so wouldn't have any REAL holding on this. And while I can see where you're going with this, because you could easily say, using the now famous physicist in front of gun example, it would STILL have to fall inside the laws of physics.
However, for quantum prediction, where you stated before, you'd have to be able to account for the millions of interactions happening at the quantum level. You can't just pick an atom in gas, and say for certainty where it's going to be. Quantum uncertainty's idea of having something that your missing points to the idea of, "If I were to drop a steel ball inside of a beaker full of gas, and maintain it's total security from the outside, there's no way of perfectly calculating how that effects it based on the millions of reactions it would first have to go through on the atomic level. And predicting it on a much lower level would only multiply the idea. So it's not magic, it's just an inability to calculate vast things. You can try all you like to predict it, but there's no way to calculate everything in there, since one thing would react to another several hundred times before it settled down.
And once again to that multiple world's theory, it still had to hold inside of our laws of physics. Anything will happen within reason. It's just there's an infinite amount of moments from when the doctor sets the gun down to when it goes off.
And any physicist worth it's salt would've read that book by now.