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More precisely, let $h(t,x)$ denote the height function of TASEP at position $x$ and time $t$; we provide an explicit formula for \\begin{equation*} \\mathbb{P}(h(t,y_1)\\leq s_1, \\ldots, h(t,y_m)\\leq s_m). \\end{equation*} The formula presented is well-suited for the scaling limit analysis. 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