I think it’s very likely that there is life elsewhere in the Universe. I also haven’t ever seen any convincing evidence that they have visited the Earth. I think it’s unlikely for several reasons:
1. According to known physics, space travel is limited by the speed of light. The exception may be wormholes but (according to my admittedly limited understanding of the subject) the energies required for traveling large distances via this method are insanely large and therefore very unlikely (although not completely impossible I don’t think). This means that it would take a VERY long time to travel here from even our closest neighboring systems.
2. We tend to think of ourselves as being pretty interesting and important as a species. To an alien race with the technological capabilities to travel those distances, we are probably very insignificant, and almost certainly not worth the effort required to make the journey to visit/study/conquer.
3. Some have theorized that once any civilization gets technologically advanced enough, there is a very high likelihood that they will annihilate themselves via wars, conflicts, catastrophic failures of technology, or via exhausting all of the natural resources required for survival. This theory ultimately suggests that the human race will likely suffer the same fate one day in the distant future. The implication is that it’s exceedingly unlikely that there are any intelligent species that have survived their “technological adolescence” phase to reach the point where they can both utilize incredibly powerful technology to visit Earth and not have wiped themselves out.
There are other reasons as well, but those are the ones that stick out in my mind. As for evidence, it’s important for me to follow the principle that extraordinary claims require extraordinary evidence. Magicians are a great example of how easily it is to deceive even exceptionally smart people. I’m not going to believe the girl in the box vanished and then reappeared without the word of several independent experts who have inspected the box she was standing in. This is partly why video evidence is so weak, if we took things at face value based on footage, then we would all believe in magic.
Cameras suffer from several problems that make them unreliable as the sole means of evidence. Forced perspective is a great example, not to mention if images are doctored. What would convince me is verification from multiple independent reliable sources.