The electric power system in Europe is undergoing rapid transformation due to the integration of intermittent and distributed energy sources. This change impacts system operations and the utilization of the system assets. Therefore, there is a growing need to assess the security of electricity supply. In Europe, however, conducting thorough analyses is hindered by the absence of failure data for generation and transmission assets. To overcome this limitation, we use generator and transmission unavailability data from the ENTSO-E transparency platform and quantify plant-specific availabilities of the European power system key assets. In particular, we apply Markov processes and compute the steady-state probabilities of generators, internal lines, interconnectors, transformers, and substations from transition rates estimated for outage events. We found that within the European power system, internal power lines fail and need maintenance less frequently than interconnectors with neighboring power systems. Our analyses also demonstrate that power transformers have higher availability compared to internal lines and interconnectors. We observe that alternate-current interconnectors exhibit notably higher availability than direct-current interconnectors. Additionally, our findings indicate variations in generator availability depending on the generator technology (e.g., fossil, nuclear, hydro, PV, wind). Remarkably, generator failure and repair rates differ based on location. This paper enables further power system security assessments by computing availability parameters (i.e., failure rates, steady-state probabilities) for European generators and transmission grid assets.