jmc

Note that from $\frac{4}{7}$ to $\frac{50}{53},$ the numerator of each fraction cancels with the denominator of the fraction three terms before it. Thus, the product simplifies to $$\frac{1\cdot 2\cdot 3}{51\cdot 52\cdot 53}=\boxed{\frac{1}{23426}}.$$