Proving Existence or Non-Existence.
The existence of a thing can be conclusively proved by producing one single instance of the thing.
To put that another way: -
When the existence of a thing is denied, This can be proven wrong by producing one single instance of the thing said not to exist
The non-existence of a thing can never be conclusively proved because there is always the theoretical assumption that the thing exists but has not been seen yet or it exists in a place that can not be visited. Unless all places in the universe have been visited and are being constantly observed, we can not be absolutely certain.
From this we can say that there are only two possible statements we can make about the existence of a thing:
The thing exists.
It is unknown if the thing exists or not.
It is not possible to prove that a thing "does not exist" without further qualifying criteria.
If a thing does NOT exist it can not leave any evidence of it's non-existence. Only things that DO exist can leave evidence. From this we can derive that conclusive proof can only come from the person that claims that a thing exists. It is nonsensical to demand proof of non-existence.
Proof that an event has occurred is somewhat different.
It can not be proved conclusively that any particular event has or has not occurred but the probability of an event occurring can be estimated depending on:-
The strength of the evidence.
The volume of evidence.
The quality of evidence.
The probability of the evidence being caused by a different event.
Independent witness corroboration.
For example: -
Event 1 - President Kennedy was assassinated.
Volume of evidence - Many witnesses, Televised, A Body, Bullet wounds.
Quality of evidence - Precise forensic evidence of cause of death, ballistics evidence linked to murder weapon. Assassin's confession.
Alternative event probability - Accidental firearm discharge unlikely because of multiple hits on target, suicide unlikely because no powder burns, no weapon found near victim. Mistaken identity or wrong target unlikely …..
Independent witness corroboration - Excellent, Directly seen by hundreds, Indirectly seen by millions.
Event 2: - A talking snake convinced a genetically engineered female to eat an apple that caused her to gain knowledge of good and evil.
Volume of evidence - Contained only in one book (Genesis) of uncertain origin.
Quality of evidence - Very poor, Snakes have no physical means of talking, The interpretation of Genesis is disputed among Christians, The eating of Apples does not cause knowledge to be gained. Serious technical difficulties in remainder of this book. Contradicts accounts from other religions.
Alternative event probability - Very High, More likely to have been an illustrative or metaphorical event rather than a literal event.
Independent witness corroboration, No witnesses.
There is a very high probability that Event 1 occurred, literally, as stated.
There is a very low probability that Event 2 occurred, literally, as stated.
It is not possible to prove or disprove the occurrence of an event you can only argue for the probability of it's occurrence.
The Christians say their God exists. The onus of proof lies with the Christians. Atheists do not have to disprove because they have not made the claim.
Christians say Genesis occured. The evidence indicates otherwise and relies on the existance of a God which has not been proven.
The above statements are not absolute, many alternative hypotheses exist as to the nature of existence, perception and reality.