You need to flatten the list and convert elements to numeric values:
prob = Import["/home/Desktop/test1.txt", "Table"]// ToExpression// Flatten;
Then you can find Shanonthe Shannon Entropy (without a do
loop and initialization):
alpha = 1.1;
t = Length[prob];
shanonshannon = Sum[-prob[[i]]*Log[prob[[i]]], {i, 1, t}];
Print[{alpha, shanonshannon}]
(* {1.1,0.0000793592} *)