Simpler than you apparently think. Even trivial.
A = 1:5;
B = [1 1 1 1 0.5];
B = cumsum([0,B])/sum(B);
N = 10000;
[~,~,bin] = histcounts(rand(N,1),B);
X = A(bin);
hist(X,100)
I think you should see that the above code will work regardless of the weights, integer, non-integer. So for your other example...
B = [0.4265 1 .9361 1 0.1532]
B = cumsum([0,B])/sum(B);
N = 1000000;
[~,~,bin] = histcounts(rand(N,1),B);
X = A(bin);
hist(X,100)
With a much larger sample, you can see the sample accurately follows the desired distribution.
