Error compiling equation

My document (subfile in documentclass book) compiles perfectly, untill I add the following equation:

begin{equation} 
label{beliefupdate}
begin{split}
b_{t+1}(s') & = Pr(s'|o',a,b) 
            & = frac{Pr(o'|s',a,b)Pr(s'|a,b)}{Pr(o'|a,b} 
            & = frac{Pr(o'|s',a) sum_{sinS}Pr(s'|a,b,s)Pr(s|a,b)}{Pr(o'|a,b)} 
            & = frac{O(o',a,s') sum_{sinS}T(s,a,s')b_t(s)}{Pr(o'|a,b)}
end{split}
end{equation}

I have loaded the packages:

usepackage{amsmath}  
usepackage{amsfonts}
usepackage{amssymb} 
usepackage{physics}

renewcommand{S}{mathcal{S}}

usepackage{graphicx}
usepackage{wrapfig}

Now, Latex starts giving me warnings in two locations of the document. The first few are in this piece of code, way before the location where I enter the equation

begin{wrapfigure}{r}
    centering
    includegraphics[scale = 0.25]{images/MDP.jpg}
end{wrapfigure}

I get the error: ‘missing number, treated as zero’ and also ‘Illegal unit of measure (pt inserted)’ both about the line centering

The second batch of errors is about the line end{split} in the equation.

errors:

FIRST ERROR:

Argument of opbraces has an extra }.

par
l.151 end{split}

---

SECOND ERROR:

Runaway argument?

(o’|a,b
! Paragraph ended before opbraces was complete.

par
l.151 end{split}

---

THIRD ERROR:
Missing $ inserted.

---

I honestly don’t see where I go wrong

        & = frac{Pr(o'|s',a,b)Pr(s'|a,b)}{Pr(o'|a,b} 

        & = frac{Pr(o'|s',a,b)Pr(s'|a,b)}{Pr(o'|a,b)}