  We develop a method of modified hyper-Ramsey spectroscopy in optical clocks,
achieving complete immunity to the frequency shifts induced by the probing
fields themselves. Using particular pulse sequences with tailored phases,
frequencies, and durations, we can derive an error signal centered exactly at
the unperturbed atomic resonance with a steep discriminant which is robust
against variations in the probe shift. We experimentally investigate the scheme
using the magnetically-induced $^1$S$_0- ^3$P$_0$ transition in $^{88}$Sr,
demonstrating automatic suppression of a sizeable \num{2e-13} probe Stark shift
to below \num{1e-16} even with very large errors in shift compensation.
