People react to events around them.
If you want to make your characters more real then describe their response to events affecting them: that casual insult from a passer-by; the joyous news of a royal wedding; a near miss from a poorly driven vehicle – all of these are occurrences that might affect a character’s mood and will help to illuminate their personality. Perhaps the royal birth that everyone is so excited about is a cause for despair because it puts them that much further from the throne.
In particular, though, people react to death.
Your character might be used to dealing with insensitive co-workers or passing insults from strangers but when your character has witnessed a dozen murders the night before, they are unlikely to be cheery as they pop into the coffee shop to get a latte.
Death is something which raises our deepest fears into the light. The reaction to a death will vary depending on the relationship to the character, but even those who are remote can have a profound effect. In my own case, I remember being completely floored by Douglas Adams’ sudden death – I didn’t know him, but I enjoyed his work and felt like I shared a tribe somehow: he was one of my formative influences, and I was appalled by how young he was.
So make your characters react to these things to make them come alive.