Then later, some critical piece of evidence surfaces — say, for example, someone comes forward saying the took a video of the crime occuring. The defendant cannot be tried again for the same crime, even though new evidence would likely convict the defendant.

Double jeopardy says that if the people do not construct a case that proves beyond reasonable doubt that the defendant is guilty — remember, we’re innocent until *proven* guilty — then that defendant cannot be tried again for the same crime.

The first jeopardy is a criminal trial going full distance such that the jury comes to a decision or if the prosecution case breaks down (evidence being shown to be faulty etc) and the attorneys for the state/people withdraw their case.

Not a situation of double jeopardy when there is simply a mistrial.