Making the impossible possible
In the novel I'm writing, magical powers are an accepted part of society and yet Steve Haven still finds himself shocked by what he finds - a man who can travel miles by using a door, any door, to transport himself to a separate building, a woman with magical healing powers and children who can create light orbs. What earns his acceptance is the people behind this magic, the courageous shopkeeper, the protective mother and the loving daughter.
There's a lot of advice out there about how characters should be created. Some writers create a grid of set questions to answer about each character. Others find photos. Some just launch in and see how their characters develop. There's no right answer here. Trial and error will show you how to people your stories.
A reader will believe anything is possible if the characters in your stories are fully-fleshed out, genuine people (even if those people are green, tentacle-clad aliens). Their backgrounds, their attitudes, their slants on life will decide how your characters react. Will they fight or flee? Will they protect the small guy or join the bullies? Get to know your characters so well that you can reel off their life history in your head and they will develop a depth that your reader will love.
"Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?" Albus Dumbledore