A systematical knowledge of the satellite and hypersatellite structures of X-ray transitions is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed explanation of the complex structures of X-ray satellites and hypersatellites are crucial for understanding the X-ray emission mechanism and the hollow atom formation mechanism. In this paper, the Kα and Kβ X-ray satellite and hypersatellite structure are theoretically studied for hollow argon atoms with the relativistic multiconfiguration Dirac-Fock (MCDF) method, which includes the Breit and quantum electro-dynamics (QED) corrections. To check the applicability of the method, the transition energies and rates of the diagram lines for Ar are calculated,. and the results are in agreement with previously published data. Then the MCDF calculations of the transition energies and probabilities of Kα 1, 2 (K →L3, 2) and Kβ 1, 3 (K → M3, 2) X-ray satellites and hypersatellites, which originate from the argon atoms with additional vacancies in the L shell, are carried out. To obtain the overall profile of the K X-ray spectrum, the diagram lines are integrated with the satellites and hypersatellites on the assumption that the intensity is proportional to the corresponding transition probability and each discrete line has a Gaussian distribution profile with a full width at half maximum (FWHM) value of 20 eV. From the convoluted profile, we can obtain the dependence of the average transition energy and relative transition intensity of the satellites and hypersatellites on the initial hollow configuration. It is found that the transition energy shift increases linearly with the number of spectator vacancies in the L shell increasing. For instance, the energy shift of the Kα satellite caused by L-shell hole is about 20 eV, and that of the Kβ satellite is 48 eV. While for hypersatellite, the energy shift increases greatly due to the double ionization in the K shell. The energy shift increment of Kα and Kβ hypersatellites corresponding to L vacancy are 21 and 52 eV, respectively. Finally, four simple empirical formulae for estimating the energy shifts of the Kα, Kβ X-ray satellites and hypersatellite for Ar atom with any number of L-shells vacancies are deduced by using the least square method. These results are useful in explaining various K X-ray spectra and better understanding the collision process.