Just as numerous Martian rocks and fossils were displaced into the
space and formed the Asteroid Belt and meteorites (
http://wretchfossil.blogspot.com/2010/11/mars-produced-asteroid-belt-and.html
), a portion of the water on Mars were displaced into the space and
formed dirty ice around comets. The theory goes as follows:

1.	When heavy rocks/fossils could somehow be moved to the space to
form the asteroid belt, it is not strange that water could also be
displaced together with solid sediments into the space and formed
dirty ice of comets.

2.	There are quite a few meteorites that came from comets. Those
meteorites have been found to contain fossilized cells of Martian
origin (note 1).
So, the dirty ice around the comets should have also originated from
Mars.

Note 1: The following articles describe meteorites coming from comets
and containing Martian fossils:

1.http://journalofcosmology.com/Life100.html

2.  http://wretchfossil.blogspot.com/2010/12/ice-meteorite-contains-alien-life.html

3. http://wretchfossil.blogspot.com/2011/07/basic-reasons-why-indian-red-rains.html

4. http://arxiv.org/ftp/arxiv/papers/1104/1104.1314.pdf

5.
http://wretchfossil.blogspot.com/2010/08/nearly-all-meteorites-displayed-on-ebay.html