A cab driver does not know in advance whom he carries in his cab, as he receives the orders via computer or phone. If he picks up a man who has/carries intoxicants or a woman heading to places of impudence and debauchery, he cannot refuse taking these orders- he may be dismissed if he does so, what is the ruling of Islam in detail on this case?

Forbidding all acts including any support for committing a sin/wrongdoing is a basic in Islam. Therefore, it is neither permissible to sell grapes for those pressing wine nor to sell a weapon for those who use it to kill infallible people, nor to give a lift to a man to a pub for drinking intoxicants or having sex with a woman who is not lawful to him, etc.

This is basically according to what Allah the Almighty says, {Help ye one another in righteousness and piety, but help ye not one another in sin and rancor}.
Therefore, whenever a Muslim driver is able to avoid -during his work- what includes any support for committing sins/wrongdoings, he has to do that, and it is unlawful to allow him permission in this case.
However, he is granted the ruling of the one driven to necessity concerning what he cannot do. Moreover, he is to render his work one of shubuhat (doubtful matters), which become strong or weak depending on the frequency of such doings.
If that happened frequently in his work and prevailed in most cases, this might be reflected on the legality of his work; by means of invalidation. , He should consequently search for another job or another area to work in, so as to be more pleasing for Allah the Almighty and less exposed to what He dislikes of such situations. Allah the Almighty knows best.