One of the main objectives of the European Space Agency's Ariel telescope (launch 2029) is to understand the formation and evolution processes of a large sample of planets in our Galaxy. Important indicators of such processes in giant planets are the elemental compositions of their atmospheres. Here we investigate the capability of Ariel to constrain four key atmospheric markers: metallicity, C/O, S/O, and N/O, for three well-known, representative hot-Jupiter atmospheres observed with transit spectroscopy, i.e. HD 209458b, HD 189733b, and WASP-121b. We have performed retrieval simulations for these targets to verify how the planetary formation markers listed above would be recovered by Ariel when observed as part of the Ariel Tier 3 survey. We have considered eight simplified different atmospheric scenarios with a cloud-free isothermal atmosphere. Additionally, extra cases were tested to illustrate the effect of C/O and metallicity in recovering the N/O. From our retrieval results, we conclude that Ariel is able to recover the majority of planetary formation markers. The contributions from CO and CO2 are dominant for the C/O in the solar scenario. In a C-rich case, C2H2, HCN, and CH4 may provide additional spectral signatures that can be captured by Ariel. In our simulations, H2S is the main tracer for the S/O in hot-Jupiter atmospheres. In the super-solar metallicity cases and the cases with C/O > 1, the increased abundance of HCN is easily detectable and the main contributor to N/O, while other N-bearing species contribute little to the N/O in the investigated atmospheres.