One-step exact Grover search with a quarter of the inputs marked ($r=\frac{1}{4}\Rightarrow P_{\mathrm{marked}}=1$)

Start from $|s⟩=N^{-1/2}{\sum }_x|x⟩$, negate amplitudes at marked indices, and apply $2|s⟩⟨s|-I$. If the marked fraction is $r$, the oracle-state mean amplitude is $(1-2r)/\sqrt{N}$. Inversion about the mean therefore gives amplitudes $(1-4r)/\sqrt{N}$ on unmarked indices and $(3-4r)/\sqrt{N}$ on marked ones. The marked success probability is $r(3-4r{)}^2$. At $r=1/4$ it is exactly one: unmarked amplitudes vanish and each marked amplitude is $2/\sqrt{N}$. The output is uniform among the $N/4$ marked indices. This is an exact special case of Grover's algorithm, using one phase oracle call under the stated promise.