Aggregation of mass by perfectly inelastic collisions in a one-dimensi
onal self-gravitating gas is studied. The binary collisions are subjec
t to the laws of mass and momentum conservation. A method to obtain an
exact probabilistic description of aggregation is presented. Since th
e one-dimensional gravitational attraction is confining, all particles
will eventually form a single body. The detailed analysis of the prob
ability P-n(t) of such a complete merging before time t is performed f
or initial states of n equidistant identical particles with uncorrelat
ed velocities. It is found that for a macroscopic amount of matter (n
--> infinity), this probability vanishes before a characteristic lime
t. In the limit of a continuous initial mass distribution the exact a
nalytic form of P-n(t) is derived. The analysis of collisions leading
to the time-variation of P-n(t) reveals that in fact the merging into
macroscopic bodies always occurs in the immediate vicinity of t. For
t > t, and n large, P-n(t) describes events corresponding to the fina
l aggregation of remaining microscopic fragments.