7 Answers

It's called circumstantial evidence and it's up to the persecutor to sell the judge on the evidence. 

It can be by direct evidence, i.e., is evidence of a fact based on a witness's personal knowledge or observation of that fact. A person's guilt of a charged crime may be proven by direct evidence if, standing alone, that evidence satisfies a jury beyond a reasonable doubt of the person's guilt of that crime.

You can get arrested for just about anything... but if there is no case you will be out and free in no time!

If arrested, only ask for an attorney. The burden of proof rests on their shoulders.   Do NOT speak to any of the arresting officers.  Silence is really Golden here. 

How about with surveillance footage, you may not know it, but there may be plenty of evidence!  Just do not steal, and you will have no worries!  

Bad luck?

They must feel they have some kind of proof! It's only logical.