You asked a police officer about the requirements of probable cause? Sometimes police officers are attorneys, but generally they are not. I think you would get a much different/better discussion of reasonable suspicion/probable cause from a criminal defense attorney, or a prosecutor.
Further, police officers generally have motive to, and indeed regularly make arguments in court that probable cause exists in any given situation. In a word, asking a police officer whether probable cause exists, is in my opinion, similar to asking a car salesman whether it is time for you to purchase a new car. Depending on the salesman, the answer is probably going to be a “yes” most of the time.
It is also important to remember that the court is the final arbiter of whether probable cause or an exception to the warrant requirement exists (which is the primary issue in this instance in my opinion -Probable cause is required to affect an arrest or obtain a warrant, not conduct a warrantless entry of a house).
In a hypothetical set of facts similar to these, I would argue (emphatically!) that in the absence of other facts, an open garage and backdoor in a neighborhood that has had crime in the past is simply not enough to enter the house without a warrant. Period. If the officers heard screaming coming from within the house, then it would be a difficult ball of wax (and could fall under the public safety exception, etc).
I am not your attorney, this is not legal advice. I am just discussing an issue that seems interesting in general terms and there are no doubtless other facts which are not discussed in this blog entry.