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This paper investigates the impact of realistic propagation conditions on the achievable secrecy performance of multiple-input multiple-output systems in the presence of an eavesdropper. Specifically, we concentrate on the $κ$-$μ$ shadowed fading model because its physical underpinnings capture a wide range of propagation conditions, while, at the same time, it allows for much better tractability than other state-of-the-art fading models. By considering transmit antenna selection and maximal ratio combining reception at the legitimate and eavesdropper's receiver sides, we study two relevant scenarios $(i)$ the transmitter does not know the eavesdropper's channel state information (CSI), and $(ii)$ the transmitter has knowledge of the CSI of the eavesdropper link. For this purpose, we first obtain novel and tractable expressions for the statistics of the maximum of independent and identically distributed (i.i.d.) variates related to the legitimate path. Based on these results, we derive novel closed-form expressions for the secrecy outage probability (SOP) and the average secrecy capacity (ASC) to assess the secrecy performance in passive and active eavesdropping scenarios, respectively. Moreover, we develop analytical asymptotic expressions of the SOP and ASC at the high signal-to-noise ratio regime. In all instances, secrecy performance metrics are characterized in closed-form, without requiring the evaluation of Meijer or Fox functions. Some useful insights on how the different propagation conditions and the number of antennas impact the secrecy performance are also provided.