  The recent discovery of pressure induced superconductivity in the binary
helimagnet CrAs has attracted much attention. How superconductivity emerges
from the magnetic state and what is the mechanism of the superconducting
pairing are two important issues which need to be resolved. In the present
work, the suppression of magnetism and the occurrence of superconductivity in
CrAs as a function of pressure ($p$) were studied by means of muon spin
rotation. The magnetism remains bulk up to $p\simeq3.5$~kbar while its volume
fraction gradually decreases with increasing pressure until it vanishes at
$p\simeq$7~kbar. At 3.5 kbar superconductivity abruptly appears with its
maximum $T_c \simeq 1.2$~K which decreases upon increasing the pressure. In the
intermediate pressure region ($3.5\lesssim p\lesssim 7$~kbar) the
superconducting and the magnetic volume fractions are spatially phase separated
and compete for phase volume. Our results indicate that the less conductive
magnetic phase provides additional carriers (doping) to the superconducting
parts of the CrAs sample thus leading to an increase of the transition
temperature ($T_c$) and of the superfluid density ($\rho_s$). A scaling of
$\rho_s$ with $T_c^{3.2}$ as well as the phase separation between magnetism and
superconductivity point to a conventional mechanism of the Cooper-pairing in
CrAs.
