  We report on the first measurement of $p\Lambda$ and $pp$ correlations via
the femtoscopy method in p+Nb reactions at $\mathrm{\sqrt{s_{NN}}=3.18}
~\mathrm{GeV}$, studied with the High Acceptance Di-Electron Spectrometer
(HADES). By comparing the experimental correlation function to model
calculations, a source size for $pp$ pairs of $r_{0,pp}=2.02 \pm
0.01(\mathrm{stat})^{+0.11}_{-0.12} (\mathrm{sys}) ~\mathrm{fm}$ and a slightly
smaller value for $p\Lambda$ of $r_{0,\Lambda p}=1.62 \pm
0.02(\mathrm{stat})^{+0.19}_{-0.08}(\mathrm{sys}) ~\mathrm{fm}$ is extracted.
Using the geometrical extent of the particle emitting region, determined
experimentally with $pp$ correlations as reference together with a source
function from a transport model, it is possible to study different sets of
scattering parameters. The $p\Lambda$ correlation is proven sensitive to
predicted scattering length values from chiral effective field theory. We
demonstrate that the femtoscopy technique can be used as valid alternative to
the analysis of scattering data to study the hyperon-nucleon interaction.
