Probability DP (dynamic programming) computes expected values or probabilities instead of counts or extrema. Each dp value represents the probability or expected value at a position, and transitions have probabilities attached.
In standard DP, you might write dp[i]=min(dp[i−1]+cost1,dp[i−2]+cost2). In probability DP, you write dp[i]=p1⋅dp[i−1]+p2⋅dp[i−2] where p1 and p2 are probabilities. The observation: instead of taking min or max, you take a weighted sum. Each transition contributes proportionally to how likely it is.