  The interactions of kaons (K) and antikaons ($\mathrm{\overline{K}}$) with
few nucleons (N) were studied so far using kaonic atom data and measurements of
kaon production and interaction yields in nuclei. Some details of the
three-body KNN and $\mathrm{\overline{K}}$NN dynamics are still not well
understood, mainly due to the overlap with multi-nucleon interactions in
nuclei. An alternative method to probe the dynamics of three-body systems with
kaons is to study the final state interaction within triplet of particles
emitted in pp collisions at the Large Hadron Collider, which are free from
effects due to the presence of bound nucleons. This Letter reports the first
femtoscopic study of p$-$p$-$K$^+$ and p$-$p$-$K$^-$ correlations measured in
high-multiplicity pp collisions at $\sqrt{s}$ = 13 TeV by the ALICE
Collaboration. The analysis shows that the measured p$-$p$-$K$^+$ and
p$-$p$-$K$^-$ correlation functions can be interpreted in terms of pairwise
interactions in the triplets, indicating that the dynamics of such systems is
dominated by the two-body interactions without significant contributions from
three-body effects or bound states.
