In a particular town, the cars are of four colours only: black 40%, white 20%, red  30% and green 10%. A serious crime took place in the town and, according to the only witness, three men made their escape in a black car. The police know that, on average, witnesses are correct 80% of the time, in that, if they say a car is a certain colour, in 20% of cases it will not be that colour but one of the other three colours.
What is the probability that the get-away car was actually black?
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