In order to make this a good riddle, you need to say "What did he lose first?" 

"His job" is a reasonable answer to the question "An ex-policeman lost his house, his car and his girlfriend. What did he lose first?" This is because "what" can be anything. By saying "which one," you narrowed the range of answers. "Which one" means "either his house, his car, or his girlfriend, choose one of those three."

The reason it works as a riddle is that people hear "What did he lose first" and think it must be one of those three. After they hear the answer, then they realize that the word "what" leaves open the possibility of a different answer.

Suppose I say to my grandchildren, "What would you like for breakfast? We have eggs, pancakes, or oatmeal." If they answer "waffles." I'll say "OK, let me see if we have any."

Suppose I say to my grandchildren, "Which would you like for breakfast--eggs, pancakes, or corn flakes?" If they answer "waffles," I might say "That wasn't a choice! Eggs, pancakes or corn flakes are your choices. Which is it?"

Dan's response was a mini-lesson in the English language and he explained everything very well.
Well done Dan.
Jorge, you should send Dan $5 for the great lesson he gave you... :)

Even after making Dan's recommended (necessary) changes, I still have a problem saying that the answer is "his job".
Maybe he did not lose his job. Maybe he retired or quit, in which case the verb "lose" would be inaccurate.

He LOST his house, car, and girlfriend, but the verb "lose" is not connected with his "policeman's job".
In other words, there's nothing in the sentence that suggests that he "lost" his policeman's job.

The verb you want is "to lose." It's pronounced like "looze." The "o" sounds like the "oo" in "moon," the "s" sounds like a "z". It rhymes with "bruise," "cruise," "booze" (informal for alcoholic drink), "snooze."

"Loose" has the sibilant "s" sound, no buzz. It rhymes with "moose," "goose," "sluice," "juice," and it is an adjective meaning "not tight."

Alycia...

You don't have to sign up.

The poster meant to tell a joke and casually got a free English lesson instead??

[The sentence is not a question, so there is no need for a question mark. Also, it is considered incorrect to have more than one of the same punctuation mark, e.g., it is wrong to have more than one exclamation mark, question mark, comma, etc. ]

Can I have his luck/talent?

[Yes]

Where do I sign up?

[You wrote a funny comment. In the future, I will send you some corrections if I see any mistakes in the things you write. But usually, your writing is quite good.]