If you ask them to read a particular person's mind, they won't usually do so, so there is not much evidence that they can do what they actually say. Some will be tricksters, others seem to genuinely believe what they say. It is as well to have an open mind but also a reasonable one. You may feel yourself that you have this power. If so, perhaps it would be worth checking this out with a close relative, friend, therapist, nurse or doctor.
Thoughts can work in quite mysterious ways.
They are essential to our existence but can sometimes be confusing. It may be that something they did, which might have seemed like a sign to you, is the convincing factor. Perhaps they said something that you are sure, they could only know if they read your thoughts. It may just be that you don't feel that you need anything to back up your belief, you just know it to be true. On the other hand, you might be sure that someone else seems to know just what you have been thinking about.