Summary: The quantization of non-abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work, we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in \(\mathrm{SU}(N)\) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov’s no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger’s horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov’s no-pole condition and Zwanziger’s horizon condition.