Fun fact: as long as it was a necessary condition, it's still murder. It's no different than if you shoot someone with stage 4 cancer.

It's not automatically murder when someone's action was a necessary condition behind another's death.

For the sake of argument, suppose that we know that some action leads to a death 0.0001% of the time. In such a situation, murder would be an inappropriate charge, because a person shouldn't reasonably be expected to have known that their actions would lead to that death. For example, imagine that someone has a stress-induced heart attack as a consequence of a police encounter. Is that murder? Obviously not, even though in this example the police's existence was a necessary condition behind the cortisol spike which lead to that heart attack.

At the other end of the spectrum, if you shoot someone intentionally, you know that there's a ~50% chance that they'll die from that, so your intention to kill is implied from the act and murder is therefore appropriate.

I don't believe that 0.0001% is the correct figure for what Chauvin did to Floyd, it's certainly higher, but it's not an irrelevant question.

If Chauvin believed he was following MPD procedure (which he wasn't exactly, but it was fairly close to training materials), and that procedure leads to death only a very small % of the time, there's a plausible case for a lesser manslaughter charge there, or even no criminal charge at all in the general case where procedure was followed closely (which it wasn't here) and that procedure is generally safe.

This is incorrect. Chavin is charged with felony murder, which is when a death is the result of another felony (in this case, 2nd degree assault). All the state has to prove is the assault charge (that he intentionally took action, that action was not a justified use of force, and that the action caused harm), and that his actions were a significant cause of death. They don't have to prove intent to kill or that a reasonable person would realize it would cause death. Only that he assaulted Floyd, and that his actions did cause (not did exclusively cause) death

I don't believe it's incorrect. For the third-degree murder charge, the defendant must commit the act "evincing a depraved mind".

If the defendant thinks that they're following official protocol correctly and their training told them that that protocol was safe, then they're not "evincing a depraved mind", and are therefore not guilty of third-degree murder. The belief states of the defendant are relevant in this particular charge.

  "(a) Whoever, without intent to effect the death of any person, causes the death of another by perpetrating an act eminently dangerous to others and evincing a depraved mind, without regard for human life, is guilty of murder in the third degree and may be sentenced to imprisonment for not more than 25 years."

Supposedly, though, the jury in this case thought that Chauvin was indeed "evincing a depraved mind" (given the guilty verdict).