I'm assuming you're approaching this from a US centric point of view. If not, please ignore.
From a U.S point of view the courts have made it VERY clear that the police, and the state in general do NOT have a duty to protect you (they should, and most try, but it is not a requirement). To quote
" But there is no constitutional right to be protected by the state against being murdered by criminals or madmen. It is monstrous if the state fails to protect its residents against such predators but it does not violate the due process clause of the Fourteenth Amendment or, we suppose, any other provision of the Constitution. The Constitution is a charter of negative liberties; it tells the state to let people alone; it does not require the federal government or the state to provide services, even so elementary a service as maintaining law and order." (Bowers v. DeVito, 1982) see http://ftp.resource.org/courts.gov/c/F2/686/686.F2d.616.80-2078.80-1865.html, paragraph 6.
To continue. The state "... does not have an affirmative duty to protect individuals from private third parties" (Gonzales vs. City of Castle Rock, 2004).
If you really want an eye opener on just what the state can get away with not doing in regards to the protection of a private citizen, read the Gonzales vs. Castle Rock opinion. It's read that sounds like a bad "B" movie.
The key part of the Bowers decision, in regards to your argument is "...it does not require the federal government or the state to provide services, even so elementary a service as maintaining law and order" (Bowers v. DeVito, 1982). This doesn't (in my opinion) invalidate your argument, but you'll be hard pressed to argue that a service is, in of itself, a right, rather than a privilege.
One last point, you *DO* have the right "to not be killed by random strangers", but, as the court noted, it is up to you to claim that right. You can have Life, Liberty, and Happiness, but it's up to you to do what is necessary, within the confines of our society, to exercise those rights.
