Background: The neutron-deficient osmium isotopic chain provides a great laboratory for the study of shape evolution, with the transition from the soft triaxial rotor in $^{168}\mathrm{Os}$ to the well-deformed prolate rotor in $^{180}\mathrm{Os}$, while shape coexistence appears around $N=96$ in $^{172}\mathrm{Os}$. Therefore, the study of the Os isotopic chain should provide a better understanding of shape changes in nuclei and a detailed scrutiny of nuclear structure calculations. In this paper, the lifetimes of the low-lying yrast states of $^{170}\mathrm{Os}$ have been measured for the first time to investigate the shape evolution with neutron number.Purpose: Lifetimes of excited states in the ground-state band of $^{170}\mathrm{Os}$ are measured to investigate the shape evolution with neutron number in osmium isotopes and compare with state-of-the-art calculations.Methods: The states of interest were populated via the fusion-evaporation reaction $^{142}\mathrm{Nd}(^{32}\mathrm{S},4n)$ at a bombarding energy of 170 MeV at the ALTO facility from IPN (Orsay, France). Lifetimes of the ${2}_{1}^{+}$ and ${4}_{1}^{+}$ states in $^{170}\mathrm{Os}$ were measured with the recoil-distance Doppler-shift method using the Orsay universal plunger system.Results: Lifetimes of the two first excited states in $^{170}\mathrm{Os}$ were measured for the first time. A very small $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})/B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=0.38(11)$ was found, which is very uncharacteristic for collective nuclei. These results were compared to state-of-the-art beyond-mean-field calculations.Conclusions: Although theoretical results give satisfactory results for the energy of the first few excited states in $^{170}\mathrm{Os}$ and the $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ they fail to reproduce the very small $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$, which remains a puzzle.