Psychic power, in my belief, is a gift from the Creator. It depends upon the person, if they use it and develop it, or ignore it. I would guess that there are probably many who may have the gift, and just don't recognize it, or simply wish not to believe in it. When you have this gift, it can often be made stronger by working with it. By working with it, I am talking about serious work, and not parlor games. For instance, if you have a vision (a dream or a waking 'picture' in your mind that comes to you totally unrelated to anything you are doing at the time) of some occurance, keep a journal, and see if it comes to pass. My daughter, Kell (co-owner of SpiritKeep), has foreseen earthquakes, large fires, and plane crashes... and the crashes include something about the plane, like which airline, or country, or colors/markings on the plane. Her visions usually happen 7 to 10 days ahead of the occurrance. Most come to her in dreams, but sometimes during waking hours, as well.
Psychics are gifted in many different ways. Some can 'read' things about a person, help locate lost people, lost items, and a multitude of other different abilities.
Can anyone put psychic ability in a test tube, and prove it's existance? No. But, the power of the human mind/spirit is awesome. Each of us has a tiny fragment of the Creator within us, our 'life force' or 'consciousness'... that which makes us a living being. There is a connection of all living things to the Creator in a similar way, as if we are all connected to the vast consciousness of all living things and the Creator by an invisible thread. In a way, you might say a psychic can access this 'collective consciousness' to varying degrees. No one has all of the answers to what 'psychic power' consists of, nor can we capture it and show it for a visual verification by those who question it's existance. We can only show the fruits of the ability... for instance, by documenting a vision, and later having the event in the vision actually occur.
I hope that this viewpoint can help to answer some of your questions. This, of course, is psychic ability as I see it from my perspective, from my own personal reality. Yes, I have some psychic abilities myself, and I always seek to strengthen them, as they were a gift from my Creator, and I thank him by using them. I believe that there is awesome power in the mind, far beyond what can be imagined. But, that power in our minds comes from the connection to the vast consciousness and our connection to All That Is.