Building frequency table using tick by tick data

I am trying to calculate the conditional probability of upmove (price going up) given that the previous price movement has been up or down. This is based on transition matrix obtained in the following paper: https://www.jstor.org/stable/2283188?seq=1#metadata_info_tab_contents

The raw tick by tick data looks like this:

Stock V3 V4 V5 V6 date

A EQ 9:07:41 115.95 100 2016/01/01

A EQ 9:07:41 115.95 200 2016/01/01

A EQ 9:07:42 116 200 2016/01/01

I need to calculate probabilities using frequency table. The required probability is Pr (Price(at transaction-t) | Price(at transaction-t-1), (at transaction-t-2).......)

This sequence can vary from 1 to 10.

It'd be great if someone can help me provide the logic for how to form the transition matrix like shown in paper for different sequences varying from 1 to 10. The paper shows sequence of length 2.