  It has been traditionally hypothesized that the heavy quark (charm, $c$ and
bottom, $b$) fragmentation is universal across different collision systems,
based on the notion that hadronization as a soft process should occur at the
characteristic non-perturbative QCD scale, $\Lambda_{QCD}$. However, this
universality hypothesis has recently been challenged by the observation that
the $c$- and $b$-baryon production relative to their meson counterparts in
minimum bias proton-proton ($pp$) collisions at the LHC energies is
significantly enhanced as compared to the electron-positron ($e^+e^-$)
collisions. The conception of non-universality is unambiguously reinforced by
the latest measurement of the charged-particle multiplicity dependence of the
$b$-baryon-to-meson yield ratio, $\Lambda_b/B$, by the LHCb experiment in
$\sqrt{s}=13$\,TeV $pp$ collisions at the LHC, evolving continuously from the
saturation value in minimum bias $pp$ collisions toward the small value in
$e^+e^-$ collisions as the system size gradually reduces. We address the
multiplicity dependence of $b$-baryon production in the canonical statistical
hadronization model with input $b$-hadron spectrum augmented with many hitherto
unobserved states from quark model predictions. We demonstrate that the
decreasing trend of the $\Lambda_b/B$ toward low multiplicities can be
quantitatively understood from the canonical suppression on the yield of
$\Lambda_b$, as caused by the requirement of strict conservation of baryon
number in sufficiently small systems. We have therefore proposed a plausible
scenario for understanding the origin of the non-universality of heavy quark
fragmentation in elementary collisions.
