Video solution:

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Written solution:

Let each square have side length $1$, so the total area of the three squares is $3$. It is easier to subtract the unshaded region to the left of diagonal $AJ$ from this total.

Using the solution diagram, rectangle $EDKF$ has area $1\cdot\dfrac12=\dfrac12$, and triangle $AKJ$ has area $$\dfrac12\cdot\dfrac32\cdot2=\dfrac32.$$ Thus the unshaded area is $\dfrac12+\dfrac32=2$, so the shaded pentagon has area $3-2=1$.

The requested ratio is $\dfrac{1}{3}$.

Thus, C is the correct answer.