  Using the data samples of 102 million $\Upsilon(1S)$ and 158 million
$\Upsilon(2S)$ events collected by the Belle detector, we search for a
pentaquark state in the $pJ/\psi$ final state from $\Upsilon(1,2S)$ inclusive
decays. Here, the charge-conjugate $\bar{p}J/\psi$ is included. We observe
clear $pJ/\psi$ production in $\Upsilon(1,2S)$ decays and measure the branching
fractions to be $\mathcal{B}[\Upsilon(1S) \to pJ/\psi + anything] = [4.27 \pm
0.16(stat.) \pm 0.20(syst.)] \times 10^{-5}$ and $\mathcal{B}[\Upsilon(2S) \to
pJ/\psi + anything] = [3.59 \pm 0.14(stat.) \pm 0.16(syst.)] \times 10^{-5}$.
We also measure the cross section of inclusive $pJ/\psi$ production in $e^+e^-$
annihilation to be $\sigma(e^+e^- \to pJ/\psi + anything) = [57.5 \pm 2.1
(stat.) \pm 2.5(syst.)]$~fb at $\sqrt{s} = 10.52~\hbox{GeV}$ using an
89.5~fb$^{-1}$ continuum data sample. There is no significant $P_c(4312)^+$,
$P_c(4440)^+$ or $P_c(4457)^+$ signal found in the $pJ/\psi$ final states in
$\Upsilon(1,2S)$ inclusive decays. We determine the upper limits of
$\mathcal{B}[\Upsilon(1,2S)\to P_c^{+} + anything] \cdot \mathcal{B}(P_c^{+}\to
pJ/\psi)$ to be at the $10^{-6}$ level.
