What are the chances of warm water freezing faster than cold water? (How many percent?)
Does it have to do with container size or something in it?
The phenomenon ("warm water freezing faster than cold water") is not probabilistic. Rather, it either occurs or it doesn't depending on the precise definitions and control of all relevant conditions.
From the wikipedia page:
A reviewer for Physics World writes, "Even if the Mpemba effect is real — if hot water can sometimes freeze more quickly than cold — it is not clear whether the explanation would be trivial or illuminating." He pointed out that investigations of the phenomenon need to control a large number of initial parameters (including type and initial temperature of the water, dissolved gas and other impurities, and size, shape and material of the container, and temperature of the refrigerator) and need to settle on a particular method of establishing the time of freezing, all of which might affect the presence or absence of the Mpemba effect.