Transition probability with zero-frequency

Question

With the below code I can calculate the Markov chain probabilities per time step. However I would like to make the following change to my code:

a.) speed up the transitions: increase the number of each transition by one

AND another change in my code for

b.) speed up each transition only between specific time steps (for example 04:10-04:30)

Can this be done with Laplace smoothing

The mathematical formula for the Laplace smoothing is :

where nij represents the count of users whose activity has changed from i to j in the data, and ni represents the count of users whose activity is i at the time step k.

The mathematical formula for calculating the transition probability matrixes is:

Sample code:

library(readr)
library(markovchain)

mcListFist <-
  markovchainListFit(data = df[,], name = "df")

matrixList <- list()

for (i in 1:dim(mcListFist$estimate)) {
  myMatr <-  mcListFist$estimate[[i]]@transitionMatrix
  matrixList[[i]] <- myMatr
}

matrixList

Sample code:

df<-structure(list(`04:00` = c(1, 1, 1, 1, 1, 0, 0, 0, 0, 0), `04:10` = c(1, 
1, 0, 0, 0, 0, 0, 0, 0, NA), `04:20` = c(1, 1, 1, 0, 0, 0, 0, 
0, 1, NA), `04:30` = c(0, 0, 0, 0, 0, 0, 1, 1, 1, NA)), row.names = c(NA, 
-10L), spec = structure(list(cols = list(`04:00` = structure(list(), class = c("collector_double", 
"collector")), `04:10` = structure(list(), class = c("collector_double", 
"collector")), `04:20` = structure(list(), class = c("collector_double", 
"collector")), `04:30` = structure(list(), class = c("collector_double", 
"collector"))), default = structure(list(), class = c("collector_guess", 
"collector")), delim = ","), class = "col_spec"), problems = <pointer: 0x0000023694f01da0>, class = c("spec_tbl_df", 
"tbl_df", "tbl", "data.frame"))