Truncated Poisson Distribution probs not adding up to one

using Distributions
λ = 2.0; #Poisson parameter
zp = 0.4; #zero prob. 
dpoi = Poisson(λ)
dzip = MixtureModel([Dirac(0.0), dpoi], [zp, 1.0-zp])  #ZeroInflated ZIP
dztp = Truncated(dpoi, 1, Inf)                         #ZeroTruncated ZTP 
dzmp = MixtureModel([Dirac(0.0), dztp], [zp,1.0-zp])   #ZeroModified ZMP
####
sum(pdf(dpoi, 0:1000)) #1.0
sum(pdf(dzip, 0:1000)) #1.0
sum(pdf(dzmp, 0:1000)) #1.2734073051133634
sum(pdf(dztp, 0:1000)) #1.4556788418556055

Shouldn’t the Truncated Poisson distribution be a distribution whose probs add up to one?