Why didn't the king throw Daniel in the fiery furnace along with his three friends?

Fear and jealousy. Nebuchadnezzar made Daniel a great man and made him ruler over the whole province of Babylon and chief of the governors over all the wise men of Babylon (Daniel 2:48) because he was able to interpret the king's dream. The Chaldeans probably knew better than to go after Daniel at this time. Instead, they accused those Jews (Daniel 3:8) whom the king had set over certain affairs of the province of Babylon (Daniel 3:12), of not worshiping the image of gold.