When you have eliminated the impossible, whatever remains, however improbable, must be the truth.
~ The Sign of Four, Sir Arthur Conan Doyle
The creator of the greatest fictional detective, Sherlock Holmes, came up with this great observation on deductive reasoning: examine all the explanations, then eliminate those which could not have happened until only one remains.
There is nothing wrong with the logic in this statement. Detectives still talk about eliminating people from their enquiries, and my son even has a game "Guess Who?" which works on the same principle.
However there is more to this statement, and it is very telling. It shows people will be prepared to believe something that is totally improbable and full of inconsistencies if they consider it to be the only option on the table. It also shows that what people end up believing goes hand in hand with what they are not prepared to believe. Although some explanations will be eliminated through observation and reasoning - some are never even considered because they are deemed impossible from the outset.
Your assumptions on what is possible determines your worldview, and your worldview determines your belief. It doesn't matter how much evidence to the contrary you are presented with, if you filter that evidence though you presuppositions you will never be presented with anything that challenges your belief.
Take the darwinian theory of evolution. It doesn't matter how improbable it is, or how many unexplained stages it involves, to those who have written of anything supernatural as impossible, the fact that we are here is the only proof they need to claim that it must be true.
It is said "seeing is believing" but the "Conan Doyle" principle shows that this is often not the case. You might think that all that is required to convince someone who disbelieves in the miraculous is for them to witness a miracle, but in practice it doesn't work like that. If someone holds firm to their belief that the supernatural is impossible they will reinterpret the evidence to an alternative explanation no matter how improbable that might be. In the Gospel accounts, when Jesus presented a man born blind who could now see, there were many who preferred to believe that Jesus had found another healthy man who looked identical to the blind man, than accept that a miracle had occurred.
You see in cases like these seeing is not believing. Compelling evidence alone is not enough to persuade. What is required is a change of worldview that allows people to reach a correct conclusion from the evidence. Without this they will go away just as sceptical as when they arrived.
The ancient Greeks had a word for this change of worldview: metaknoia. It means literally to change your mind. Not to change you mind about something, but as if you had exchanged your mind - radically changing the way you think about something.
Interestingly, this is the word that gets translated as "repent" in the Bible, and was the first word used by both Jesus and John the Baptist in their message about the coming kingdom of God. "Repent for the kingdom of God is at hand." Change your assumptions about what is possible, because if you don't you will not be able to receive anything that follows.