Yeah, empathy is the ability to share the emotions of someone in a particular situation, whether or not you've literally 'been there' before. I've never starved but I feel terrible for people who are and I can vividly imagine the many levels of emotional and physical pain they go through.
I think I'm pretty empathetic - I usually feel emotional whenever I see/hear anyone in pain. With the exception of tearing up if I don't have my guard up, it's not something that changes the way I act.
But I admit I feel stronger emotion if I feel the reason for someone else's pain is logically justified. Kids being upset about anything, having a serious medical problem, being emotionally betrayed by someone they had good reasons to trust, being financially fucked, people grieving for lost loved ones, etc - I take this stuff seriously. People weeping or freaking out because their jerk boyfriend treated them badly for the umpteenth time, or they broke something they liked, or someone they barely know died - I feel bad that they are genuinely upset, but thinking 'get a grip' interferes with my empathy for them.