Reduced transition probabilities have been measured for the neutron-rich 73,74,75Ni nuclei with relativistic Coulomb excitation performed at the RIKEN Nishina Center. For the even-even Ni isotope the determined B(E2;0+→2+) value is compatible within errors with the result of a previous intermediate energy Coulomb excitation experiment, although being somewhat larger. For the odd Ni isotopes B(E2) values have been determined for the first time. In the middle νg9/2 shell nucleus 73Nithree peak candidates have been observed and tentatively assigned to the (5/2+), (13/2+), and (11/2+) excitations. Two peak candidates have been observed in 75Ni and tentatively assigned to the (13/2+) and (11/2+) levels. The measured B(E2) values are in line with the large B(E2) reported in 70Ni and at variance with the small strength measured in 72Ni. Excitation energies compare well with the result of large-scale shell-model calculations, while B(E2) values are larger than predicted. This could indicate an increasing contribution of proton excitations across the Z=28 shell closure when approaching 78Ni.