2020 Fermat Problem 25

Three real numbers x, y, z are chosen randomly, and independently of each other, between 0 and 1, inclusive. What is the probability that each of x - y and x - z is greater than -\frac{1}{2} and less than \frac{1}{2} ?

\textbf{(A)}\ \frac{3}{4}\quad \textbf{(B)}\ \frac{7}{12}\quad \textbf{(C)}\ \frac{1}{4}\quad \textbf{(D)}\ \frac{1}{2}\quad \textbf{(E)}\ \frac{2}{3}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.