Darlington pair open circuit output behaviour
A ULN2803 is usually used to drive a load of some sort connected between the output (the collectors of Q1 and Q2) and a higher voltage, typically 12V. Without a load the output will not behave as you expect. However, what you expected to happen is not what really happens.

With the input off (or 0V) transistors Q1 and Q2 will be off, and the output will "float". With a pullup resistor connected between the output and 12V the output will be pulled up to 12V. With the input on (3.3V) Q1 and Q2 will turn on and pull the output down to near 0V.

If you do not have a load or pull-up resistor on the output then when you apply 3.3V to the input the base of Q1 will be clamped to around 1.2V due to the two forward biased base-emitter diodes in Q1 followed by Q2. The base-collector diode in Q1 will also be forward biased, so the 1.2v on the base of Q1 appears on the collector of Q1, minus another 0.6V diode drop. Hence you see approx 0.6V on the collector.