If I sit too close to our fire pit, my clothes will smell like fire for days. Singe some hair, and you'll know it by the smell. However, these three walk out of a roaring furnace hot enough to kill the people throwing them into it and they don't even smell of fire. They are miraculously unharmed, and Nebuchadnezzar takes this all in and praises God. Not too long ago, he was willing to kill anyone not worshiping a false idol. All of a sudden, through this dramatic act, Nebuchadnezzar is willing to fight to the death for anyone who speaks against the one true God.
Our lives are transformed by God. Hearts can change, minds can change. We hear stories about dramatic transformations that still go on today -- I was listening to an old speech by Ravi Zacharias earlier and he was talking about a dramatic transformation at a chaotic prison due to the influence of one faithful disciple. We love to hear these stories, and some people I talk to feel somewhat envious for not having a dramatic story.
To answer that, I point to Shadrach, Meshach, and Abednego. The King here undergoes a dramatic transformation, but it's only after seeing the steadfast faithfulness of these three. They quite simply trusted God in every situation, and through their witness, others were brought to believe in God.
There's a place for everyone in the story. God never gives up on anyone, and God uses each of us to tell a dramatic story of grace and love.