Why was Napoleon exiled and not executed?

Why did his winning adversaries choose to isolate him on an island? Twice. At the time, killing a king (which the French just did during the Revolution) was considered dangerous. It created unrest in the population and would give "bad ideas" to the mob. Napoleon's adversaries were monarchs who cared for the second-order effects of his execution.

But why did they think of Napoleon as a king? He was a commoner after all, even though he declared himself Emperor. Mainly because Napoleon was still loved by the French people, especially the military. They didn't want to stir another rebellion.