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In an urn there are 10 balls marked with the numbers 1-10.

4 balls are being chosen randomly without replacement.

It is known that on the 4th ball that was taken out, there was a number which was larger than the number on any of the previous 3 balls taken.

What is the probability that on the 4th ball the number was 10 ?

I thought of conditional probability, the intersection should be in my opinion:

(9/10)*(8/9)*(7/8)*(1/7)

I am not sure it's right and anyway I don't know what to do with the probability of the 4th being larger than the other 3....

thanks !