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The present study focuses on the application of a picosecond (ps) TALIF technique in krypton (Kr) at variable pressure (0.1-10 mbar). The laser intensity (I, units W.cm$^{-2}$) is tuned between 1 and 480 MW.cm$^{-2}$, and the depletion of the density of the Kr 5p'[3/2]$_2$ fluorescing state through photoionization (PIN) and amplified stimulated emission (ASE) is investigated. This is done by combining TALIF experiments with a simple 0D numerical model. We demonstrate that for a gas pressure of 3 mbar and 15 < $\le$ 480 MW.cm$^{-2}$, a saturated fluorescence signal is obtained, which is largely attributed to PIN, ASE being negligible. Also, a broadening of the two-photon absorption line (i.e. 4p$^6$ $^1$S0$\to$5p'[3/2]$_2$) is recorded due to the production of charged species through PIN, inducing a Stark effect. For I$\le$15 MW.cm$^{-2}$, though, PIN is significantly limited, the absorption line is noticeably narrowed, and the quadratic dependence of the TALIF signal intensity versus the laser energy is obtained. Thus, in this case, the investigated Kr TALIF scheme, using the 5p'[3/2]$_2\to$5s[3/2]$_1$ fluorescence channel, can be used for calibration purposes in ps-TALIF experiments. These results are of interest for fundamental research since most ps-TALIF studies performed in Kr do not investigate in detail the role of PIN and ASE on the depletion of the Kr 5p'[3/2]$_2$ state density. Moreover, this work contributes to the development of ps-TALIF for determining absolute densities and quenching coefficients of H and N atoms in plasmas. This is useful in numerous plasma-based applications (e.g. thin film synthesis, biomedical treatments, plasma-assisted combustion, ...), for which the knowledge of the density/kinetics of reactive atoms is essential.