You cannot conclusively prove that something does not exist – the best you can do is show that the lack of evidence likely means that the something probably doesn’t exist.
Take, for example, Big Foot. It would be easy enough to prove that he does exist, just either bring him in as proof or get some high quality photos and/or other evidence (e.g. scat, bones, etc) that proves he exists. On the other hand though, the best we can do to prove that big foot does not exist is to use the fact that conclusive evidence showing his existence doesn’t exist but that could be countered using the numerous possible reasons as to why we cannot gather that evidence (e.g. he is good at avoiding human contact and good at not leaving any traces behind).
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