This simple logic probe has both LEDs on with no signal at the input but due to the nor gates connected to the probe, indicates correctly when a high or low signal is present. It also works correctly for pulse trains. Normally both LEDs are forward biased and therefore on, powered by the 12V supply. When a logic "high" is present at the probe, IC1a's output goes low sending IC1b's output high. This turns off LED1 but forward-biases (and turns on) LED2. Conversely, a logic "low" at the probe will send IC1b low, turning LED1 on and LED2 off.
circuit from http://www.extremecircuits.net/2010/05/simple-logic-probe.html