See for example this paper.
Covering by random intervals and one-dimensional continuum percolation
C. Domb, J. Stat. Phys. Vol. 55(1-2), 1989
and also
Exact solution of a one-dimensional continuum percolation model
A. Drory, Phys. Rev. E Vol. 55(4), 1997
among other works, including many by the second author above.