"Evidence" is not adequately defined.
Alright, let's do this. Everyone here is (or, should be, I hope) familiar with the basic idea of inductive logic. Maybe they've never heard that term before, but I'm sure they agree with the idea "The sun has come up over the horizon in the east every morning of my life. Every person I've ever asked has said that every time they've seen the sun rise, it rose in the east. Never has the sun been seen to rise in the west, north or south. Therefore, the sun will rise in the east tomorrow morning."
That's induction: the idea that things that have happened are indictative of things that will happen. If we approach the idea more analytically, we get three parts to induction: The "what I thought before I used induction", "what I thought after I used induction" and the "what I saw to make me use induction". Or, in more formal terms, your prior probability, your posterior probability and your
evidence. Even more formally, we have the following mathmatical relationship between them:
Posterior Probability = P[Idea|Evidence] = Prior Probability * Evidence Ratio = P[Idea] * P[Evidence|Idea] / P[Evidence]
An example:
We have a room with some people in it. 25% of the people in the room are male and the rest are female. You know for a fact that 75% of the women speak French while only 50% of the men do. You're told this all in advance, and know it to be accurate. Someone slips a note through the door, written in French. What are the odds that a man wrote it?
P[French] = P[Male] * P[French|Male] + P[Female] * P[French|Female] = 68.75%
P[Male|French] = P[Male] * P[French|Male] / P[French] = 25% * 50% / 68.75% = 18.181818...% = 2/11
The evidence for a hypothesis is the ratio between the probability of what you've seen so far if the hypothesis is true and the probability of seeing what you've seen so far in general. If you're more likely to see what you've seen if the hypothesis is true than you would in general, then you should beleive that hypothesis more. And if your hypothesis suggests that you shouldn't have seen what you saw before, you should start doubting it.
So, to restate LordExumius's prior post:
Faith is belief in a hypothesis with certainty out of proportion to the ratio between how likely the world is to be how it is according to the hypothesis and how likely the world is to be like it is in general. Or, in short, "Faith is belief without evidence."