Allow me to offer this as an experimental concept. In our pop-culture society, which has chosen to base all its knowledge of reality on emotional subjectivism, we often find ourselves arguing rational and evidence against pure experiential emotionalism i.e., fact against feeling.
If I may take a moment to mention the fact that our modern day world is literally saturated with information of all possible sorts literally available to us in mere seconds and at the touch of a button. The fact that so many people are perfectly willing to base all of their opinions on nothing but emotion and personal experience, so willing to tell themselves that we cannot ever really know that something is true with any real certainty, is absolutely shameful. People should be utterly embarrassed for taking such a position, such an easy way out of putting any effort whatsoever into formulating worldviews.
As an aside, allow me to mention that the only facts that such people see as being absolute is that there are no absolutes. For instance your claim to having been given the knowledge regarding the only way to salvation is no more nor less an absolute truth claim than their claim that you do not have any such knowledge (for more on this issue see our article Monophobia).
Back to the experiment, I have spent hours talking to skeptics about the Christian faith while discussing various modes of evidence such as history, manuscripts and archeology. I employed the usual arsenal of ways by which to share the faith, the issue is that all of this was met not with an equal or greater amount of evidence and rational but rather with an expression of disbelief of what I was saying based on nothing at all besides dislike of the ultimate conclusions, emotion and all of the basic subjective reasons.
This made me think that next time I am witnessing to someone like that I will simply tell them that I believe because it just feels right and I just had an experience that made me think that it was true. Then how do you know that it is true? They may ask, to which I would simply respond I just do!
Of course, this should not be the end of the conversation. It would actually be a good exercise because you can point out how obviously unsatisfying your claim of basing your faith on pure goose bumps and wishful thinking is. Take it from there and get into reasons and evidence.
Finally, let us make something clear; emotional-subjective-experiences are good and dry intellect and factual proofs are good as well. They are both, in a sense, the two extremes; either one is likely to be unsatisfying without the other and both are best served with a good balance of the other.