  Quantum contextuality describes scenarios in which it is impossible to
explain the experimental evidence in terms of a measurement independent
reality. Here, I introduce a three-path interferometer in which all five
contexts needed for a demonstration of contextuality are realized in sequence.
It is then possible to observe a paradoxical situation where the paths
connecting input ports to their corresponding output ports appear to be blocked
by destructive interference. It is shown that the conditional currents observed
in weak measurements provide a consistent explanation of the paradox,
indicating that weak values might help to bridge the gap between wavelike
propagation effects and local particle detection.
