Darius believed in Daniel's God, but he knew from all other things that it was impossible for someone to survive a night with lions. verse sixteen says, So the king gave the order, and they brought Daniel and threw him into the lions’ den. The king said to Daniel, “May your God, whom you serve continually, rescue you!”(NIV). thus, he believes, but does not know.
another point for you is this, verse eighteen says, Then the king returned to his palace and spent the night without eating and without any entertainment being brought to him. And he could not sleep.(NIV)
and later in verse 19 and 20, At the first light of dawn, the king got up and hurried to the lions’ den. When he came near the den, he called to Daniel in an anguished voice, “Daniel, servant of the living God, has your God, whom you serve continually, been able to rescue you from the lions?”(NIV)
and in the end, if you know how it goes, Daniel lives and goes on to see and record his visions.