Points randomly chosen on a segment.

Let us consider a segment of \(AB\) of a given length \(k,\) where \(k\) is an arbitrary positive number. We pick two points \(C\) and \(D\) on the segment randomly, so that they divide the given segment into three shorter segments of positive length. What is the probability that the three shorter segments can be used to form a triangle?

Note: This problem -that was suggested to me by my nephew Joey- is not intended to be original.

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