How does the Ternary Operator work in this piece of code?

I have a small piece of code of a function to set color that looks like this:

private Color color = Color.CYAN;
public void setColor(Color c) {
		color = c != null ?c :color;
		repaint();
	}

Does it means something like this?

color = c;
if (c != null) {
        color = c;
        } else {
        c = color;
}

I can't really wrap my head around this piece of code. Please enlighten me.

It's more like

if (c != null) {
    color = c;
} else {
    color = color;
}

which, in turn, because color = color; essentially does nothing, is the same as:

if (c != null) {
    color = c;
}