For cache analytical modeling, the stack distance theory is widely utilized to predict LRU-cache behaviors. Typically, the stack distance histogram collecting is implemented by profiling memory references. However, the profiled memory references merely reflect instruction fetching and load/store executions, which only represent the memory accesses to first-level (L1) caches. That is why these traces cannot be applied directly to construct stack distance histograms for downstream (L2 and L3) caches.Therefore, this paper proposes a stack distance probability model to extend the stack distance theory to the multi-level LRU cache behavior predictions. The inputs of our model are the L1 cache stack distance histograms and the multi-level LRU cache configurations. The outputs are the L2 and L3 cache stack distance histograms, with which the conflict misses in L2 and L3 caches can be quantified quickly and precisely.15 benchmarks chosen from Mobybench 2.0, Mibench I and Mediabench II are used to evaluate the accuracy of our model. Compared to the simulation results from Gem5 in AtomicSimpleCPU mode, the average absolute error of predicting cache misses in the I/D shared L2 cache is less than 5% while that of estimating the L3 cache misses is less than 7%. Furthermore, contrast to the time overhead of Gem5 AtomicSimpleCPU simulations, our model can speed up the cache miss prediction about x100 on average.