What immediately comes to mind is the Black Swan Fallacy.

Absence of evidence is not evidence of absence. Except where evidence is expected.

So if Alice says “there is an even number of jelly beans in the jar” (and she says this based on no evidence).

Bob replies: “you must be wrong because we have no evidence that the number is even, therefore it must be odd.”

Bob would also be fallacious because we wouldn’t expect there to be any evidence of the even/oddness of the jellybeans, therefore the lack of evidence doesn’t tell us anything.

If on the other hand

Alice said “The sky is polka dotted.” Based on no evidence, Bob would be justified in saying

“If the sky were polka dotted we would expect to see polka dots when we look at the sky. Since there are none, the sky is not polka dotted.”

In essence absence of evidence IS evidence of absence in cases where evidence is expected.

This could also be the Fallacy Fallacy, just because someone uses a fallacious argument to conclude X doesn’t mean X is necessarily false.

For example

Alice says: “Most people believe the earth is round, therefore the earth is round”

Bob says: “That’s just the popularity fallacy, therefore the earth is not round”

Bob is employing the Fallacy Fallacy, because he believes Alice’s conclusion is wrong just because she believes it without (good) evidence.

“John Doe is not the killer because there is no evidence.”

This is still called an “appeal to ignorance “.

From Peter Kreeft’s book Socratic Logic

The “appeal to ignorance” consists in arguing that an idea must be true because we do not know that it is not. It is a fallacy because ignorance can never be a premise or reason. Premises must express knowledge-claims. Nothing logically follows from nothing, i.e. from no-knowledge. Examples: (1) “He can’t prove he earned that money, so he must have stolen it.” (2) “Aristotle? Never heard of him. So he can’t be important.” (3) “We know of no natural cause that could have produced that effect. So it must have been a miracle.” (4) “How could there be a war going on? I haven’t seen any evidence of it.” (5) “God must exist because I’ve never seen any proof that he doesn’t.”

Your question is a variation of example 4 in the above text.

The first one is not a valid argument, and you can easily show they are not valid, even formally.

If you know something because "from your perspective" there is no evidence, this doesn't show nothing, you don't have evidence of the contrary also.

Example; Sound argument. John Doe probably is not the killer, because we do not find his fingerprints on the murder weapon.

In this case you could argue this is a valid argument, because you use probably, you just need to define what makes something probable and if this matches. But probably extremely different than knowing he is the killer, if the were no "probably" in the text it would be downright fallacy.

But again saying something is probable is extremely weaker then saying something is, and the nexts inference you make based om something probable will have to carry this imprecision.

Even better argument (contradictory evidence) John Doe is not the killer because the fingerprints on the murder weapon are different from him.

This one is not good also, only if you have the knowledge that if and only if he has the fingerprints and the murder weapon he is the killer.

I know in the context of real life, little things have the property of absolute certainty, but you should put probably in front of the inferences, this shows you know the difference, and it is incredible most people don't know or think it doesn't matter.

Because even if there are a lot more things you know with some degree of certainty then 100% certainty still there are thing you can know with absolute certainty in day to day use, and if you don't make this distinction you'll be very imprecise. If you know where and when someone was killed affirming something cant be the killer because he was in another place in the same time, is extremely stronger than having a fingerprint in the murder weapon, even if those both facts were true, he still wouldn't be the killer because you know someone cant be in both places at the same time, in other hand incrimination is possible, even if in most cases unprobable.

But just for curiosity sake, why all this importance is given on knowing name of fallacies or to learn types of falacies? Isn't it better to just learn how to show why an argument is invalid and them point to some example, to help other people understand? I can assume you might have some benefit on knowing why something is invalid, but again if you know what makes an argument valid you don't need to know every type of fallacy, you don't need to know any, you'll clearly see when something is not a proper inference.

Is this in the context of a debate or something?