  This text presents one of the first successful applications of a rare events
method for the study of multistability in a turbulent flow without stochastic
energy injection. The trajectories of collapse of turbulence in plane Couette
flow, as well as their probability and rate of occurrence are systematically
computed using \emph{Adaptive Multilevel Splitting} (AMS). The AMS computations
are performed in a system of size $L_x\times L_z=24\times 18$ at Reynolds
number $R=370$ with an acceleration by a factor $\mathcal{O}(10)$ with respect
to DNS and in a system of size $L_x\times L_z=36\times 27$ at Reynolds number
$R=377$ with an acceleration by a factor $\mathcal{O}(10^3)$. The AMS results
are validated with a comparison to DNS in the system of size $L_x\times
L_z=24\times 18$. Visualisations in both systems indicate that turbulence
collapses because the self sustaining process of turbulence fails locally. The
streamwise vortices decay first in streamwise elongated holes, leaving
streamwise invariant streamwise velocity tubes that experience viscous decay.
These holes then extend in the spanwise direction. The examination of more than
a thousand of trajectories in the $(E_{c,x}=\int u_x^2/2\,{\rm
d}^3\mathbf{x},E_{c,y-z}=\int (u_y^2/2+u_z^2/2)\,{\rm d}^3\mathbf{x})$ plane in
the system of size $L_x\times L_z=24\times 18$ confirms the faster decay of
streamwise vortices and shows concentration of trajectory. This hints at an
instanton phenomenology in the large size limit. The computation of turning
point states, beyond which laminarisation is certain, confirms the hole
formation scenario and shows that it is more pronounced in larger systems.
Finally, the examination of non reactive trajectories, where a hole opens then
closes, indicates that hole opening and closing are distinct processes. Both
the vortices and the streaks reform concomitantly when the laminar holes close.
