In which situation is neurotransmitter release from a presynaptic cell most likely to stimulate an action potential in a postsynaptic cell?

In a postsynaptic cell/neuron where a depolarizing change in the membrane potential surpasses the threshold.

Explanation:

Generally, in an excitable cell, the neurotransmitter binding opens the ligand-gated channels at the synapse. Here only the entrance of the ions will not stimulate the action potential. They must exceed the threshold. Hence, an action potential will only get incited when in a postsynaptic cell/neuron, a depolarizing change in the membrane potential surpasses the threshold.