Define the states Let = The maximum amount of money the robber can get from houses to . If you define your dp like this, the base case is simple. Now think of the Transition (the formula that computes each state from earlier states).
Take time to understand this concept thoroughly. Work through small examples by hand. The pattern will become clear with practice. Once you internalize it, you will recognize similar problems immediately. The state at position i depends only on earlier positions. This makes the DP well-defined.