We study the collective spontaneous emission of three identical two-level atoms initially prepared in the excited states by measuring Glauber's third-order photon correlation function. Assuming two atoms at subwavelength distance from each other such that they are subject to the dipole-dipole interaction while the third one is located several wavelengths away, we observe super- and subradiant decay alike, depending on the direction of observation. Unlike the case where no remote atom is introduced or no conditional measurements are performed, the spontaneous emission behavior of the conditioned three-atom system is strongly modified, i.e., differing from the single-atom and the canonical two-atom configuration. The conditional measurements associated with the three-photon correlation function in combination with the dipole-dipole interaction between the adjacent atoms lead to quantum interference among the different decay channels allowing one to engineer the spontaneous emission in space and time.