To explicit Chocolate's answer and by the way answer gibbon.
ありじゃないか should be read as "[something]じゃないか" that you would basically translate as "Doesn't/Isn't it [something] ?".
Even as a negative form, turned as a question with the ？/か/かな, it becomes a positive wonder. Like a question tag. Plus, you should not see it as a question directed to you, more like the person speaking to him/herself and just expressing his/her wonder out loud.
The [something] itself, can be positive or negative, it does not matter. It will mean "Doesn't/Isn't it [something] ?"
To Gibbon> でしょう／だろう can be used for similar cases. Ex: you don't find something, it would be 100% normal to say "どこでしょう？" speaking to yourself or someone else.